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Tamil Nadu Board of Secondary EducationHSC Science Class 11

Evaluate nrnrn!r!(n-r)! when for any n with r = 2

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Question

Evaluate `("n"!)/("r"!("n" - "r")!)` when for any n with r = 2

Sum
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Solution

For any n with r = 2

`("n"!)/("r"!("n" - "r")!)= ("n"!)/(2!("n" - 2)!)`

= `("n"("n" - 1)("n" - 2)!)/(1 xx 2 xx ("n" - 2)1)`

= `("n"("n" - 1))/2`

= `("n"^2 - "n")/2`

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Chapter 4: Combinatorics and Mathematical Induction - Exercise 4.1 [Page 166]

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Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 4 Combinatorics and Mathematical Induction
Exercise 4.1 | Q 15. (iii) | Page 166

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