If 20 C r -20 C r -10- then 18 C r is equal toA- None of theseB- 4896C- 816D- 1632

The correct option is C 816 r + r 10 = 20 [∵ ^nC_x = ^nC_y⇒ n = x + y or x = y] ⇒ 2r 10 = 20 ⇒ 2r = 30 ⇒ r = 15 Now ^18C_r = ^18C_15 ∴^18C_15 = n!/(n r)! r ...

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Standard XII

Mathematics

nCr Definitions and Properties

If 20 C r =20...

Question

If $^{20} C_{r} =^{20} C_{r - 10},$ then $^{18} C_{r}$ is equal to

4896

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816

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1632

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None of these

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Solution

The correct option is B
816

$r + r - 10 = 20$
$[∵^{n} C_{x} =^{n} C_{y} \Rightarrow n = x + y o r x = y] \Rightarrow 2 r - 10 = 20 \Rightarrow 2 r = 30 \Rightarrow r = 15$
Now $^{18} C_{r} =^{18} C_{15}$
$∴^{18} C_{15} = \frac{n!}{(n - r)! r!} = \frac{18!}{(18 - 15)! 15!} = \frac{18 \times 17 \times 16 \times 15!}{3 \times 2 \times 15!} = \frac{18 \times 17 \times 16}{3 \times 2} = 816$

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If 20Cr=20Cr−10, then 18Cr is equal to

The correct option is B 816 r+r−10=20 [∵ nCx=nCy⇒n=x+y or x=y]⇒2r−10=20⇒2r=30⇒r=15 Now 18Cr=18C15 ∴18C15=n!(n−r)!r!=18!(18−15)!15!=18×17×16×15!3×2×15!=18×17×163×2=816

If $^{20} C_{r} =^{20} C_{r - 10},$ then $^{18} C_{r}$ is equal to