If 18 C15 + 2( 18 C16) + 17 C16 + 1 = n C3, then n is equal to

Explanation: 18 C 15 + 2 ( 18 C 16 ) + 17 C 16 + 1 = n C 3 ⇒ 18 C 15 + 18 C 16 + 18 C 16 + 17 C 16 + 1 = n C 3 ⇒ 18 C 15 + 18 C 16 + 18 C 16 + 17 C 16 + 17 C 17 = n C 3 ⇒ 19 C 16 + 18 C 16 + 18 C 17 = n C 3 ⇒ 19 C 16 + 19 C 17 = n C 3 ⇒ 20 17 = n C 3 ⇒ n = 20

Question:

If ¹⁸C15 + 2(¹⁸C16) + ¹⁷C16 + 1 = ⁿC3, then n is equal to

WBJEE

Updated On: Apr 27, 2024

(A) 19
(B) 20
(C) 18
(D) 24

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The Correct Option is B

Solution and Explanation

Explanation:

^{18} C_{15} + 2 (^{18} C_{16}) +^{17} C_{16} + 1 =^{n} C_{3}

\Rightarrow^{18} C_{15} +^{18} C_{16} +^{18} C_{16} +^{17} C_{16} + 1 =^{n} C_{3}

\Rightarrow^{18} C_{15} +^{18} C_{16} +^{18} C_{16} +^{17} C_{16} +^{17} C_{17} =^{n} C_{3}

\Rightarrow^{19} C_{16} +^{18} C_{16} +^{18} C_{17} =^{n} C_{3}

\Rightarrow^{19} C_{16} +^{19} C_{17} =^{n} C_{3}

\Rightarrow 20_{17} =^{n} C_{3} \Rightarrow n = 20

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If 18C15 + 2(18C16) + 17C16 + 1 = nC3, then n is equal to

The Correct Option is B

Solution and Explanation

Top Questions on Geometric Progression

Questions Asked in WBJEE exam

If ¹⁸C15 + 2(¹⁸C16) + ¹⁷C16 + 1 = ⁿC3, then n is equal to