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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

(a) n = 9, r = 0

$rightwards double arrow$ $fraction numerator straight n factorial over denominator straight r factorial space left parenthesis straight n minus straight r right parenthesis factorial end fraction equals fraction numerator 9 factorial over denominator 0 factorial space 9 factorial end fraction space equals space fraction numerator 9 factorial over denominator 9 factorial end fraction equals 1$ (∵ 0! = 1)

(b) n = 8, r = 1

$rightwards double arrow$ $space space space fraction numerator straight n factorial over denominator straight r factorial space left parenthesis straight n minus straight r right parenthesis factorial end fraction space equals space fraction numerator 8 factorial over denominator 1 factorial space 7 factorial end fraction space equals space fraction numerator 8 cross times 7 factorial over denominator 7 factorial end fraction space equals space 8$

(c) n = 9, r = 9

$rightwards double arrow$ $fraction numerator straight n factorial over denominator straight r factorial space left parenthesis straight n minus straight r right parenthesis factorial end fraction space equals space fraction numerator 9 factorial over denominator 9 factorial space 0 factorial end fraction space equals space fraction numerator 9 factorial over denominator 9 factorial end fraction equals 1$ (∵ 0! = 1)

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Short 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.