First slide

Combinations

Question

In an election, the number of candidates is one greater than the persons to be elected. If a voter can vote in 254 ways, the number of candidates is

Moderate

A

7
B

10
C

8
D

6

Solution

Let there be n candidates. Then
$\begin{array}{l} ^{n} C_{1} +^{n} C_{2} + \dots +^{n} C_{n - 1} = 254 \\ \Rightarrow 2^{n} - 2 = 254 \\ or 2^{n} = 2^{8} or n = 8 \end{array}$

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