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NCERT Class XI Mathematics - Permutations and Combinations - Solutions

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Question : 10 of 41
Marks: +1, -0
Evaluate n!(n−r)!\frac{n!}{(n-r)!} , when
(i) n = 6, r = 2 (ii) n = 9, r = 5.
Solution:  
(i) 6!(6−2)!\frac{6!}{(6-2)!} = 6!4!\frac{6!}{4!} = 6×5×4!4!\frac{6\times5\times4!}{4!} = 30
(ii) 9!(9−5)!\frac{9!}{(9-5)!} = 9!4!\frac{9!}{4!} = 9×8×7×6×5×4!4!\frac{9\times8\times7\times6\times5\times4!}{4!} = 15120
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