First slide

Combinations

Question

Rakshit is allowed to select $(n + 1)$ or more books out of $(2 n + 1)$ distinct books. If the number of ways in which he may not select all of them is 255, then value of n is

Moderate

A

3
B

4
C

5
D

11

Solution

Use $^{2 n + 1} C_{n + 1} +^{2 n + 1} C_{n + 2} + \dots +^{2 n + 1} C_{2 n} = 2^{2 n} - 1$
$4^{n} - 1 = 255 \Rightarrow 4^{n} = 256 \Rightarrow n = 4$

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