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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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Long 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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Short Answer Type

39.
If (n+1)! = 30 (n - 1)!, find value of n.

space space left parenthesis straight n plus 1 right parenthesis factorial space equals space 30 space left parenthesis straight n minus 1 right parenthesis factorial

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left parenthesis straight n plus 1 right parenthesis space left parenthesis straight n right parenthesis space left square bracket left parenthesis straight n minus 1 right parenthesis factorial right square bracket space equals space 30 space left parenthesis straight n minus 1 right parenthesis factorial

rightwards double arrow

(n + 1) (n) = 30

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straight n squared plus straight n minus 30 space equals space 0

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(n + 6) (n - 5) = 0

rightwards double arrow

space space space space space space space space space space straight n equals negative 6 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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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.

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

39.
If (n+1)! = 30 (n - 1)!, find value of n.