# There are 4 candidates for the post of a chairman, and one is to be elected

Question:

There are 4 candidates for the post of a chairman, and one is to be elected by votes of 5 men. In how many ways can the vote be given?

Solution:

Let suppose 4 candidates be $C_{1}, C_{2}, C_{3}, C_{4}$ and 5 men be $M_{1}, M_{2}, M_{3}, M_{4}, M_{5}$

Now $M_{1}$ choose any one candidates from four $\left(C_{1}, C_{2}, C_{3}, C_{4}\right)$ and give the vote to him by any 4 ways

Similarly, $M_{2}$ choose any one candidates from four $\left(C_{1}, C_{2}, C_{3}, C_{4}\right)$ and give the vote to him by any 4 ways

Similarly, $M_{3}$ choose any one candidates from four $\left(C_{1}, C_{2}, C_{3}, C_{4}\right)$ and give the vote to him by any 4 ways

Similarly, $M_{4}$ choose any one candidates from four $\left(C_{1}, C_{2}, C_{3}, C_{4}\right)$ and give the vote to him by any 4 ways

And $M_{5}$ choose any one candidates from four $\left(C_{1}, C_{2}, C_{3}, C_{4}\right)$ and give the vote to him by any 4 ways

So total numbers of ways are $4 \times 4 \times 4 \times 4 \times 4=1024$