M L Aggarwal Solutions for Chapter: Permutations and Combinations, Exercise 9: CHAPTER TEST

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 atleast one girl and one boy?

Determine the number of ways of choosing $5$ cards out of a deck of $52$ cards which include at least one king.

In how many ways can $2$ men, $4$ women, $3$ boys and $3$ girls be selected from $6$ men, $8$ women, $4$ boys and $5$ girls if no restrictions are imposed?

In how many ways can $2$ men, $4$ women, $3$ boys and $3$ girls be selected from $6$ men, $8$ women, $4$ boys and $5$ girls if a particular man and woman must be selected?

How many $6-$letter words containing $4$ consonants and $2$ vowels can be formed using the letters of the word $\mathrm{GANESHPURI}$ so that the vowels occur together?

Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the seating arrangement can be made.

Find the number of words which can be formed by taking two alike and two different letters from the word $\mathrm{COMBINATION}$.

How many words can be formed by taking $4$ letters at a time out of the letters of the word $\mathrm{MATHEMATICS}$?