Permutations And Combinations

Question
CBSEENMA11014069

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

Solution

(a) n = 6, r = 2  
rightwards double arrow                  fraction numerator straight n factorial over denominator left parenthesis straight n minus straight r right parenthesis factorial end fraction equals fraction numerator 6 factorial over denominator 4 factorial end fraction equals fraction numerator 6 cross times 5 cross times 4 factorial over denominator 4 factorial end fraction space equals space 6 cross times 5 space equals 30
(b) n = 7, r = 7
rightwards double arrow                     fraction numerator straight n factorial over denominator left parenthesis straight n minus straight r right parenthesis factorial end fraction space equals space fraction numerator 7 factorial over denominator 0 factorial end fraction space equals space 7 factorial space equals space 7 cross times 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 space equals space 5040   (∵ 0! = 1)
(c) n = 9, r = 0
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Some More Questions From Permutations and Combinations Chapter

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.