MCQ Subject: Probability & Permutation Combination

Ram has 5 different books. He wants to arrange 3 of them on a shelf. Which of the following best describes the difference between the number of ways he can select AND arrange the books (permutation) versus just select the books (combination)?

Five colleagues – Amit, Ritu, Sam, Lena, and Jack – are randomly arranged in a line. What is the probability that Amit and Ritu are always next to each other?

In how many ways can 3 men and 3 women be arranged in a line such that no two women are adjacent?

A committee of 5 is to be formed from 8 men and 4 women. How many ways can the committee have at least 2 women?

A committee of 3 must include at least 1 woman. From 4 men and 3 women, how many ways can this committee be formed?

What is the probability that all vowels in the word ‘PROBABILITY’ appear together when its letters are arranged randomly?

In a group of 4 men, what is the probability that exactly 2 men have birthdays in the same month and the other 2 have birthdays in different months, with no month having more than 2 birthdays?

A box contains 5 red and 3 blue balls. If 2 balls are drawn without replacement and the first ball drawn is red, what is the probability that the second ball is also red?

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?