NCERT Solutions for Chapter: Permutations and Combinations, Exercise 1: EXERCISE

A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red.

A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they must all be of the same colour

In how many ways can a football team of $11$ players be selected from $16$ players always including $2$ particular players.

In how many ways can a football team of $11$ players be selected from $16$ players always excluding $2$ particular players?

A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has no girls.

A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least one boy and one girl.

A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least three girls.

A candidate is required to answer $7$ questions out of $12$ questions which are divided into two groups, each containing $6$ questions. He is not permitted to attempt more than $5$ questions from either group. He can choose the seven questions in $650$ ways.