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General
Easy

Question

If  left parenthesis n plus 1 right parenthesis P subscript 5 colon to the power of n P subscript 5 equals 3 colon 2then n is:

  1. 8
  2. 14
  3. 10
  4. 6

Hint:

To find the value of n in left parenthesis n plus 1 right parenthesis P subscript 5 colon to the power of n P subscript 5 equals 3 colon 2 we will first use the formulaP with r below and n on top equals fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction then after putting the values in the formula we will get the value of n.

The correct answer is: 14


    Given, left parenthesis n plus 1 right parenthesis P subscript 5 colon to the power of n P subscript 5 equals 3 colon 2
    rightwards double arrow fraction numerator begin display style fraction numerator left parenthesis n plus 1 right parenthesis factorial over denominator left parenthesis n plus 1 minus 5 right parenthesis factorial end fraction end style over denominator begin display style fraction numerator n factorial over denominator left parenthesis n minus 5 right parenthesis factorial end fraction end style end fraction equals 3 over 2
rightwards double arrow fraction numerator left parenthesis n plus 1 right parenthesis factorial over denominator left parenthesis n minus 4 right parenthesis factorial end fraction cross times fraction numerator left parenthesis n minus 5 right parenthesis factorial over denominator n factorial end fraction equals 3 over 2
rightwards double arrow fraction numerator left parenthesis n plus 1 right parenthesis n factorial over denominator left parenthesis n minus 4 right parenthesis left parenthesis n minus 5 right parenthesis factorial end fraction cross times fraction numerator left parenthesis n minus 5 right parenthesis factorial over denominator n factorial end fraction equals 3 over 2
rightwards double arrow fraction numerator n plus 1 over denominator n minus 4 end fraction equals 3 over 2
rightwards double arrow 2 left parenthesis n plus 1 right parenthesis equals 3 left parenthesis n minus 4 right parenthesis
rightwards double arrow 2 n plus 2 equals 3 n minus 12
rightwards double arrow n equals 14

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    If blank to the power of n P subscript 5 equals to the power of n P subscript 6  then n is :

    Given, blank to the power of n P subscript 5 equals to the power of n P subscript 6
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rightwards double arrow n minus 5 equals 1
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    If blank to the power of 10 P subscript r equals 5040 then r is :

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    rightwards double arrow fraction numerator 10 factorial over denominator left parenthesis 10 minus r right parenthesis factorial end fraction equals 5040
rightwards double arrow fraction numerator 10 cross times 9 cross times 8 cross times 7 cross times 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator left parenthesis 10 minus r right parenthesis factorial end fraction equals 5040
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rightwards double arrow 6 factorial equals open parentheses 10 minus r close parentheses factorial
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rightwards double arrow r equals 4

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    Given, blank to the power of 10 P subscript r equals 5040
    rightwards double arrow fraction numerator 10 factorial over denominator left parenthesis 10 minus r right parenthesis factorial end fraction equals 5040
rightwards double arrow fraction numerator 10 cross times 9 cross times 8 cross times 7 cross times 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator left parenthesis 10 minus r right parenthesis factorial end fraction equals 5040
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