M. Tyra Solutions for Chapter: Permutation and Combination, Exercise 1: Exercises

A candidate is required to answer $6$ out of $10$ questions which are divided into groups, each containing five questions. In how may ways can he answer the questions, if he is not allowed to attempt more than $4$ questions from a group?

A committee of $8$ students is to be formed out of $5$ boys and $8$ girls. In how many ways can it be done so that the no. of girls is not less than the no. of boys?

From $6$ gentlemen and $4$ ladies a committee of $5$ is to be formed. In how many ways can this be done if the committee is to include at least one lady?

A candidate is required to answer $6$ out of $10$ questions which are divided into two groups each containing $5$ questions and he is not permitted to attempt more than $4$ from each group. In how many ways can he make up his choice?

How many different groups can be selected for playing tennis out of $4$ ladies and $3$ gentlemen there being one lady and one gentleman on each side?

In how many ways can a group of $5$ men and $2$ women be made out of a total of $7$ men and $3$ women?

A team of $5$ children is to be selected out of $4$ girls and $5$ boys such that it contains at least $2$ girls. In how many different ways can the selection be made?

On a shelf there are four books on Economics, three on Management and four on Statistics. In how many different ways can the books be arranged so that the books on Economics are kept together?