Find-the-value-of-r-if-10-C-r-10-C-2r-1-

Question Number 209281 by Tawa11 last updated on 06/Jul/24

Find the value of r, if \overset{10}{} C_{r} = \overset{10}{} C_{2 r + 1}

Commented by klipto last updated on 06/Jul/24

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

^{10} C_{r} =^{10} C_{9 - 2 r}

∴ r = 9 - 2 r

r + 2 r = 9, r = 3

or

if r = 2 r + 1, r = 10 - (2 r + 1), r = 10 - 2 r - 1

r + 2 r = 9, 3 r = 9, r = 3

klipto - quanta

Commented by mr W last updated on 06/Jul/24

p l e a s e u s e “ {a n s w e r}^{″} i n s t e a d o f

“ {c o m m e n t}^{″} w h e n y o u w a n t t o a n s w e r

a q u e s t i o n .

Answered by A5T last updated on 06/Jul/24

\frac{10!}{r! (10 - r)!} = \frac{10!}{(10 - 2 r - 1)! (2 r + 1)!}

\Rightarrow (10 - 2 r - 1)! (2 r + 1)! = r! (10 - r)!

2 r + 1 ⩽ 10 \Rightarrow r ⩽ 4 \Rightarrow r = 3

Commented by Tawa11 last updated on 06/Jul/24

Thanks sir . I appreciate .

Answered by A5T last updated on 06/Jul/24

r = 2 r + 1 o r r = 10 - (2 r + 1) \Rightarrow r = 3

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