If Find value of n. from Mathematics Permutations and Combinat

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 Multiple Choice QuestionsShort Answer Type

31.

Compute:

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32.

Compute:

fraction numerator 6 factorial over denominator 3 factorial end fraction

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33.

Compute:

fraction numerator 1 over denominator 6 factorial end fraction plus fraction numerator 1 over denominator 7 factorial end fraction space



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34.

Compute:

fraction numerator straight n factorial over denominator left parenthesis straight n minus 2 right parenthesis factorial end fraction



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35.

Find x, if fraction numerator 1 over denominator 6 factorial end fraction plus fraction numerator 1 over denominator 7 factorial end fraction equals fraction numerator straight x over denominator 8 factorial end fraction

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 Multiple Choice QuestionsLong Answer Type

36.

Evaluate:  fraction numerator straight n factorial over denominator straight r factorial space left parenthesis straight n minus straight r right parenthesis factorial end fraction comma when

(a) n = 6, r = 2,  (b) n = 6, r = 4, (c) n = 9, r = 4

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37.

Evaluate:  fraction numerator straight n factorial over denominator left parenthesis straight n minus straight r right parenthesis factorial end fraction comma when:

(a) n = 6, r = 2,  (b) n = 7, r = 7, (c) n = 9, r = 0

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38.

Evaluate:  fraction numerator straight n factorial over denominator r factorial space left parenthesis straight n minus straight r right parenthesis factorial end fraction comma when:

(a) n = 9, r = 0,  (b) n = 8, r = 1, (c) n = 9, r = 9

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 Multiple Choice QuestionsShort Answer Type

39.

If (n+1)! = 30 (n - 1)!, find value of n.

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40.

If fraction numerator straight n factorial over denominator 2 factorial space left parenthesis straight n minus 2 right parenthesis factorial end fraction colon space fraction numerator straight n factorial over denominator 4 factorial space left parenthesis straight n minus 4 right parenthesis factorial end fraction equals space 2 space colon space 1

Find value of n.


space space space space space space fraction numerator straight n factorial over denominator space 2 factorial space left parenthesis straight n minus 2 right parenthesis factorial end fraction colon fraction numerator straight n factorial over denominator 4 factorial left parenthesis straight n minus 4 right parenthesis factorial end fraction space equals space 2 space colon space 1

rightwards double arrow    space space space space space space fraction numerator straight n factorial over denominator 2 factorial left parenthesis straight n minus 2 right parenthesis factorial end fraction cross times fraction numerator 4 factorial left parenthesis straight n minus 4 right parenthesis factorial over denominator straight n factorial end fraction equals 2 over 1

rightwards double arrow            fraction numerator 4 cross times 3 cross times 2 factorial cross times left parenthesis straight n minus 4 right parenthesis factorial over denominator 2 factorial left parenthesis straight n minus 2 right parenthesis left parenthesis straight n minus 3 right parenthesis cross times left parenthesis straight n minus 4 right parenthesis factorial end fraction equals 2 over 1

rightwards double arrow                           fraction numerator 12 over denominator left parenthesis straight n minus 2 right parenthesis space left parenthesis straight n minus 3 right parenthesis end fraction equals 2

rightwards double arrow                                 (n - 2) (n - 3) = 6

rightwards double arrow                                   space space straight n squared minus 5 straight n plus 6 equals 6

rightwards double arrow                                         space space space straight n squared minus 5 straight n equals 0

rightwards double arrow                                                n (n - 5) = 0

rightwards double arrow                                          straight n equals 0 space not an element of space straight N comma space straight n space equals space 5 space element of space straight N

Hence, n = 5
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