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MAT Exam 2025 Paper

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Question : 70 of 150

Marks: +1, -0

In an election, a voter may vote for any number of the seven candidates but not greater than the number to be chosen. There are seven candidates, and four are to be chosen. In how many possible ways can a person vote?

78 ways
89 ways
98 ways
107ways

Solution:

Concept:

Selecting any

1, 2, 3

, or

4

candidates from

7

using combinations.

Explanation:

A voter may choose

1, 2, 3

, or

4

candidates out of

7

.

Number of ways to choose

r

candidates from

7

is

{}^{7}C_{r}

.

So total possible ways are:

{}^{7}C_{1} + {}^{7}C_{2} + {}^{7}C_{3} + {}^{7}C_{4}

= 7 + 21 + 35 + 35 = 98

Thus, a person can vote in

98

different ways.

Answer:

C.

98

ways

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