If 20Cr = 20Cr−10, then the value of 18Cr is:

Engineering

Mathematics

Permutation and Combination Basic Definitions

Total Number of Combinations

Question

If ²⁰C_r = ²⁰C_r−10, then the value of ¹⁸C_r is:

1632

816

4896

5432

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Given ²⁰C_r = ²⁰C_r−10

We Know ⁿC_r = ⁿC_n−r

⇒ r + (n − r) = n

⇒ r + r − 10 = 20

⇒ 2r = 30

⇒ r = 15

⇒ ¹⁸C_r = ¹⁸C₁₅

$\Rightarrow \frac{18!}{15! \times 3!}$

$\Rightarrow \frac{18 \times 17 \times 16}{3 \times 2 \times 1}$

⇒ 48 × 17

⇒ 816

Hence the correct answer is 816.