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Evaluate nrnrn!r!(n-r)! for n = 15, r = 10

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Question

Evaluate `("n"!)/("r"!("n" - "r")!)` for n = 15, r = 10

Sum
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Solution

n = 15, r = 10

∴ `("n"!)/("r"!("n" - "r")!) = (15!)/(10!(15 - 10)!)`

= `(15!)/(10! xx 5!)`

= `(15 xx 14 xx 13 xx 12 xx 11 xx 10!)/(10! xx 5 xx 4 xx 3 xx 2 xx 1)`

= 3003

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Chapter 3: Permutations and Combination - Exercise 3.2 [Page 49]

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Balbharati Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
Chapter 3 Permutations and Combination
Exercise 3.2 | Q 4. (iii) | Page 49
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