if-n-C-5-n-C-11-find-18-C-n-

Question Number 41824 by Tawa1 last updated on 13/Aug/18

if \overset{n}{} C_{5} = \overset{n}{} C_{11} find \overset{18}{} C_{n}

Answered by $@ty@m last updated on 13/Aug/18

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

\Rightarrow r = 5

& n - r = 11 \Rightarrow n = 16

\Rightarrow^{18} C_{n} =^{18} C_{16} =^{18} C_{2} = 153

Commented by Tawa1 last updated on 13/Aug/18

God bless you sir

Answered by tanmay.chaudhury50@gmail.com last updated on 13/Aug/18

\frac{n \times (n - 1) \times (n - 3) \times (n - 4)}{5!} = \frac{n \times (n - 1) \dots \times (n - 10)}{11!}

(n - 5) (n - 6) (n - 7) (n - 8) (n - 9) (n - 10) = 11 \times 10 \times 9 \times 8 \times 7 \times 6

n = 16

18 c_{16} = \frac{18 \times 17}{2} = 153

Commented by Tawa1 last updated on 13/Aug/18

God bless you sir

Answered by malwaan last updated on 13/Aug/18

n = 5 + 11 = 16

∴ \underset{n}{\overset{18}{C}} = \underset{16}{\overset{18}{C}} = \frac{18 \times 17}{2 \times 1} = 9 \times 17

= 153

Commented by Tawa1 last updated on 13/Aug/18

God bless you sir

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