If-n-C-12-n-C-8-then-n-

Question Number 72441 by kouidri last updated on 28/Oct/19

If^{n} C_{12} =^{n} C_{8}, then n =

Commented by mathmax by abdo last updated on 29/Oct/19

C_{n}^{12} = C_{n}^{8} \Leftrightarrow \frac{n!}{(12)! (n - 12)!} = \frac{n!}{8! (n - 8)!} \Rightarrow 8! (n - 8)! = 12! (n - 12)! \Rightarrow

8! (n - 8) (n - 9) (n - 10) (n - 11) (n - 12)! = 12.11.10.9.8! (n - 12)! \Rightarrow

\Rightarrow (n - 8) (n - 9) (n - 10) (n - 11) = 12.11.10.9 \Rightarrow n = 20

Answered by JDamian last updated on 28/Oct/19

n = 20

Answered by $@ty@m123 last updated on 29/Oct/19

^{n} C_{r} =^{n} C_{n - r}

A T Q

\Rightarrow r = n - r + 4

\Rightarrow 2 r = n + 4

H e r e, r = 12

∴ n + 4 = 24

\Rightarrow n = 20

Commented by JDamian last updated on 29/Oct/19

R e a l l y ?^{12} C_{12} \neq^{12} C_{8}

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