MCQ Subject: Probability & Permutation Combination

How many ways can 5 people be arranged in a line if two specific individuals must not be adjacent?

In a class of 30 students, 12 are boys and 18 are girls. If 5 students are selected at random for a project, what is the probability that at least 3 are girls?

In how many ways can 5 people (A, B, C, D, E) be arranged in a row such that A is always to the left of B and C is always to the right of D?

A committee of 3 is to be selected from 4 men and 3 women. How many combinations are possible if at least one woman must be included?

A committee of 5 members is to be formed from 4 men and 3 women. If at least one woman must be included, how many different committees can be formed?

A committee of 4 people is to be formed from 3 men and 4 women. What is the probability that the committee consists of exactly 2 men and 2 women?

A committee of 3 is to be formed from 4 men and 3 women. If the probability that a particular man is always included and a particular woman is never included is 1/10, what is the total number of ways to form the committee?

A committee of 3 with distinct roles is formed from 4 men and 3 women. What is the probability of having at least one woman?

A committee of 5 is to be formed from 3 men and 4 women, with exactly 2 men. How many ways can this be done?

A committee of 3 members is to be formed from 5 men and 3 women. How many ways can this be done if the order of selection does not matter?