Maths-
General
Easy

Question

The number of different signals that can be made by 5 flags from 8 flags of different colours is :

  1. 6720    
  2. blank to the power of 8 end exponent C subscript 5 end subscript    
  3. 8 to the power of 5 end exponent    
  4. 5 to the power of 8 end exponent    

Hint:

We are provided with 8 flags of different colours and  5flags. We need to find the total number of signals that can be made by the number of arrangements of  flags by taking 5flags at a time. Arranging things is called permutation, thus we can clearly say that the given question is based on the topic “permutation”. Here we have to arrange flags taken 5flags at a time which is equivalent to filling 8flags placed out of 5flags. For that we have the formula of permutation: 

P presuperscript n subscript r equals fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction.

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The correct answer is: 6720


     Detailed solution
    We have been told that there are 8flags of different colours by taking 5flags at a time. Thus the total number of flags n=8and flags to be taken at a time r=5
    By applying the permutation formula  = P presuperscript n subscript r space equals space P presuperscript 8 subscript 5 space equals space fraction numerator 8 factorial over denominator left parenthesis 8 minus 5 right parenthesis factorial end fraction space equals space 6720

    Thus, the number of different signals that can be made by 5 flags from 8 flags of different colours is 6720.

    Each of the different arrangements which can be made by taking some or all of a number of things at a time is called permutation. The number of permutation without any repetition states that arranging n objects taken r at a time is equivalent to filling r places out of things =n(n1)(n2)......(nr1ways = 
    equals fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction equals P presuperscript n subscript r.
    P presuperscript 8 subscript 5 equals 8 cross times 7 cross times 6 cross times 5 cross times 4 equals 6720
    Thus we can say that the permutation concerns both the selection and the arrangement of the selected things in all possible ways.

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