Question

There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. The number of ways in which the votes can be given is

Answer 1

ince, there are 4 candidates, there are 4 choices for the required post. Now, determine the number of people who can vote. Multiply the choices each voter can make as this will give us the number of ways votes can be given to the candidates.

Complete step-by-step answer:
We are given that there are 4 candidates for the post of a lecturer in Mathematics and one it to be selected by votes of 5 men.
There are 4 candidates and 5 men who will vote for the candidates.
We have to find the number of ways in which votes can be given.
Each of the men who will vote has 4 choices.
And all the 5 men have 4 choices and choices are independent of the choice of other men.
That is, the same name can be repeated.

This implies that the total number of ways in which 5 men can vote for 4 candidates is $4 \times 4 \times 4 \times 4 \times 4 = {4^5}$
That is there are ${4^5} = 1024$ ways in which the votes can be given.

Note: We have a fundamental principle of counting for solving this question. Here, the vote by each of the men is compulsory, that’s why the choices are multiplied. When there are $n$ choices to be made by $m$ people, there are ${n^m}$ways of doing it.