Question
How many different nine digit numbers can be formed from the number 2,2,3,3,5,5,8,8,8 by rearranging its digits so that the odd digits occupy even position ?
- 16
- 36
- 60
- 180
Hint:
Here we need to find the total number of nine digit numbers that can be formed using the given digits. We will count the number of even places present for the odd digits and then we will find the number of odd places present for the even digits. Then we will find the number of ways to arrange the odd digits and then we will find the number of ways to arrange the even digits and to get the final answer, we will multiply both of them.
The correct answer is: 60
Detailed Solution
Here we need to find the total number of nine digit numbers that can be formed using the given digits i.e. 2, 2, 3, 3, 5, 5, 8, 8, 8.
![X minus X minus X minus X minus X](data:image/png;base64,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)
![H e r e comma space s y m b o l space left parenthesis negative right parenthesis space space i s space f o r space t h e space e v e n space p l a c e s space a n d space left parenthesis X right parenthesis space space i s space f o r space t h e space o d d space p l a c e s space o f space t h e space d i g i t space n u m b e r.](data:image/png;base64,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)
The digits which are even are 2, 2, 8, 8 and 8.
![N u m b e r space o f space e v e n space d i g i t s space equals 5](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM4AAAAQCAYAAABeK0CbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAABOhJREFUeNrtWnFEnVEUvzJ5MpEkycTMJJlIJpPETDJ5IpOZZMzMZDIySfbHmEwm2T8zk0xM+mNmxkySTGSSPImZTJJIkiSj3cvv2+5O59zvfq/nvdW+w1Hfveeee86555x77imlYsgU5Gksjc3w/8K2xk5hbg8Okk3IxZ5RoVnjFnBJ45lT6hvcWRznfP7Vsz10IAsXNKY0zghzi1lWIBd7RgUTJGsaa/BddUqDhjuL45wPXWu+Z/+hwIkESY1vNI5qvMjMjWdZgVzsGRXaToCMJ+Es2uB7JzJwBjT2amzS+ESYk77D6Ez9P6xxQ+O6xhbMF2kcQpmzo/ERWdun8THW7Guc0ljG7Gv4T4BmVWOjINddjfOg6w2xR4nGVxp3QW8SSiJE3zBwySk5z2fLXr66PgTda5RExr7dnjKexVltYw+z1wijJ6d7gcZBjZsR1g6QcojS9kHPn8J8zgPnLTKLYq5Ne477dtENwFk7UNpUaPyOAJjWeAPj52DsUmvtNxiqCPXwEJP5CnHtt1rl0hIjlympnmk872GLIvDswr6F2HfQopkkB94RwjNMTlOuLJA1Jijm0tC1G0HTCPnLYdsCjybHFNE7cOxkyFmfwXn24neDPXD4ZJr+ZILmpcb8DL9VXG+WyIGzAgMHWeCqNbdszVFa5RhfQcYsInRrMAg3XmatrWKcb4eMDZKbysB7YuwVZHRfGMSh23AefBSxy7kIPMPkpA/mL+QcfHW9w+xvbp3iEBn7hYzOnTcd62cqlYCuLGTtMhIqhVmif7ZKtQP42Qf4wVlXptmzvitQmnBz9FuF0BUIdAWO9dIeCRI4eSgpSsjYjuWAEi+XLTaZsiyBvVQafH3kDALlktWtm05D112hieEj6w/GSTg9ubF1JjA5eXz9yUC7xq/WDZvtxk8tEoIJ7EqO6DKuaBs+wYh0jqNVx6DjxiWaetxg9hruCp712E+CWqGz6KufZN8wORWSVTt+X4C+mdC13kPWGhKoLp50zNdmkh2nHXKVgfeUK/NnsFTj4JokYwdqYhs6ceXTOY42oPeh8xmXaHqQAQJoRX3sAomXBBLPB6QUicLXR04D91COJZG4VIZ09ZHVlLJjnmvp2HHWdljVjQQJvO1u5bDbts8Nmi7KbTKWj+w+TGrm50yHpg5X9W3C846wV9j4MB6oVJ5FUi/Xk8ezr24uaEZtS8uLFLmuJT2UkPHnPOha0HRYUn/+NpQJXX1skBQCc4zRk/JrVXy7eozZl641/nTfwzamw3kzR0FTjUbVEZgkLc8AXsJZW0grcRTOVILvEYaHxNNnfBIPyOBhWI6xLmZdCrdBHpoN5vHc4LGfq7Y1TYrrZO8+Tz0kCJMzaOeazPYuTR5RbU73TlkBW4vGwxqzlvIzTZsNa635OYG1jSFrRxAULqiDbMVZCJJJJKk8YDOChm0ubTGPYQNXUAsmSKv2IzoP05aDUR4ST5/xDWSxFbQzF4R2ZdDtmgFdislw0n4uaACvAzwMuyLoodKUM4BtZLhM6uoraykcZx+NiiZhLTdmzmsVNpvHu2BTHf23Grq2CgF2SLqD2xj7ifdNZZZul3bL77ZwC9epGDICJShNY3CXN+OxGWKwa3JzCz2NTfEbzG3wwnp/1qHbVxmbJgZl1f5tsRn+guDfdMzfbPbQXKk+rcr+AmyvqSxTGH+JAAABQ3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5OPC9taT48bWk+dTwvbWk+PG1pPm08L21pPjxtaT5iPC9taT48bWk+ZTwvbWk+PG1pPnI8L21pPjxtbz4mI3hBMDs8L21vPjxtaT5vPC9taT48bWk+ZjwvbWk+PG1vPiYjeEEwOzwvbW8+PG1pPmU8L21pPjxtaT52PC9taT48bWk+ZTwvbWk+PG1pPm48L21pPjxtbz4mI3hBMDs8L21vPjxtaT5kPC9taT48bWk+aTwvbWk+PG1pPmc8L21pPjxtaT5pPC9taT48bWk+dDwvbWk+PG1pPnM8L21pPjxtbz4mI3hBMDs8L21vPjxtbz49PC9tbz48bW4+NTwvbW4+PC9tYXRoPtFE6MIAAAAASUVORK5CYII=)
The digits which are odd are 3, 3, 5 and 5.
![N u m b e r space o f space o d d space d i g i t s space equals 4](data:image/png;base64,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)
We have to arrange the odd digits in even places.
![N u m b e r space o f space w a y s space t o space a r r a n g e space t h e space o d d space d i g i t s space i n space 4 space e v e n space p l a c e s space equals fraction numerator space 4 factorial over denominator 2 factorial cross times 2 factorial space end fraction](data:image/png;base64,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)
On finding the value of the factorials, we get
![N u m b e r space o f space w a y s space t o space a r r a n g e space t h e space o d d space d i g i t s space i n space 4 space e v e n space p l a c e s space equals space fraction numerator 4 cross times 3 cross times 2 cross times 1 over denominator 2 cross times 1 cross times 2 cross times 1 end fraction](data:image/png;base64,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)
On further simplification, we get
![N u m b e r space o f space w a y s space t o space a r r a n g e space t h e space o d d space d i g i t s space i n space 4 space e v e n space p l a c e s space equals 6](data:image/png;base64,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)
Now, we have to arrange the even digits in odd places.
![N u m b e r space o f space w a y s space t o space a r r a n g e space t h e space e v e n space d i g i t s space i n space 5 space o d d space p l a c e s space equals fraction numerator 5 factorial over denominator 2 factorial cross times 3 factorial end fraction](data:image/png;base64,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)
On finding the value of the factorials, we get
![N u m b e r space o f space w a y s space t o space a r r a n g e space t h e space e v e n space d i g i t s space i n space 5 space o d d space p l a c e s space equals fraction numerator 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator 2 cross times 1 cross times 3 cross times 2 cross times 1 end fraction](data:image/png;base64,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)
On further simplification, we get
![N u m b e r space o f space w a y s space t o space a r r a n g e space t h e space e v e n space d i g i t s space i n space 5 space o d d space p l a c e s space equals 10](data:image/png;base64,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)
![T o t a l space n u m b e r space o f space 9 space d i g i t s space n u m b e r space equals space 6 cross times 10 space equals space 60](data:image/png;base64,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)
![H e n c e comma space t h e space r e q u i r e d space n u m b e r space o f space 9 space d i g i t space n u m b e r s space equals 60](data:image/png;base64,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)
Here we have obtained the total number of 9 digit numbers using the given digits. While finding the number of ways to arrange the odd digits in 5 even places, we have divided the 4! by 2! because the digit 3 were occurring two times and the digit 5 were occurring 2 times. Here we can make a mistake by conserving the number of even digits 4 and the number of odd digits 5, which will result in the wrong answer.
Related Questions to study
A person predicts the outcome of 20 cricket matches of his home team. Each match can result either in a win, loss or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct, is equal to :
A person predicts the outcome of 20 cricket matches of his home team. Each match can result either in a win, loss or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct, is equal to :
The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is (repetition is not allowed) :
Alternatively, we can use the formula for the sum of numbers as
We can also solve this problem by writing all the possible numbers and finding the sum of them which will be time taking and make us confused. We should know that the value of the digits is determined by the place where they were present. We should check whether there is zero in the given digits and whether there are any repetitions present in the numbers. Similarly, we can expect problems to find the sum of numbers formed by these digits with repetition allowed.
The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is (repetition is not allowed) :
Alternatively, we can use the formula for the sum of numbers as
We can also solve this problem by writing all the possible numbers and finding the sum of them which will be time taking and make us confused. We should know that the value of the digits is determined by the place where they were present. We should check whether there is zero in the given digits and whether there are any repetitions present in the numbers. Similarly, we can expect problems to find the sum of numbers formed by these digits with repetition allowed.
Total number of divisors of 480, that are of the form 4n + 2, n
0, is equal to :
We can also solve this question by writing 4n + 2 = 2(2n + 1) where 2n + 1 is always an odd number. So, when all odd divisors will be multiplied by 2, we will get the divisors that we require. Hence, we can say a number of divisors of 4n + 2 form is the same as the number of odd divisors for 480.
Total number of divisors of 480, that are of the form 4n + 2, n
0, is equal to :
We can also solve this question by writing 4n + 2 = 2(2n + 1) where 2n + 1 is always an odd number. So, when all odd divisors will be multiplied by 2, we will get the divisors that we require. Hence, we can say a number of divisors of 4n + 2 form is the same as the number of odd divisors for 480.
If 9P5 + 5 9P4 =
, then r =
If 9P5 + 5 9P4 =
, then r =
Assertion (A) :If
, then ![A equals 3 comma B equals 2](data:image/png;base64,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)
Reason (R) :![fraction numerator P x plus q over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis end fraction equals fraction numerator P a plus q over denominator left parenthesis x minus a right parenthesis left parenthesis a minus b right parenthesis end fraction plus fraction numerator P b plus q over denominator left parenthesis x minus b right parenthesis left parenthesis b minus a right parenthesis end fraction](data:image/png;base64,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)
Assertion (A) :If
, then ![A equals 3 comma B equals 2](data:image/png;base64,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)
Reason (R) :![fraction numerator P x plus q over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis end fraction equals fraction numerator P a plus q over denominator left parenthesis x minus a right parenthesis left parenthesis a minus b right parenthesis end fraction plus fraction numerator P b plus q over denominator left parenthesis x minus b right parenthesis left parenthesis b minus a right parenthesis end fraction](data:image/png;base64,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)
A particle is released from a height. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively
A particle is released from a height. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively