Permutations And Combinations

Question
CBSEENMA11014070

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

Solution

(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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