Home
Class 12
MATHS
Find the numbers of ways in which 5 girl...

Find the numbers of ways in which 5 girls and 5 boys can be arranged in a row if no two boys are together.

Text Solution

Verified by Experts

In this example, there is no condition for arranging the girls. Now, 5 girls can be arranged in 5! Ways
XGXGXGXGXGX
When girls are arranged, six gaps are generated as shown above with 'X'.
Now, boys must occupy the places with 'X' marked, so that no two boys are together.
Therefore, five boys can be arranged in these six gaps inn `.^(6)P_(5)` ways.
Hence, total number of arrangement is `5!xx.^(6)P_(5)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the number of ways in which 5 girls and 5 boys can be arranged a n row if boys and girls are alternative.

The number of the ways in which 5 girls and 3 boys can be seated in a row so that no two boys are together is

In how many ways can 5 girls and 3 boys be selected in a row so that no two boys are together ?

Find the number of ways in which 12 different beads can be arranged to form a necklace.

The number of ways in which 6 mean and 5 women can dine at a round table if no two women are to sit together is given by :

The number of ways in which 6 boys and 6 girls can sit alternatively is :

The number of ways in which 5 boys and 3 girls can he seated in a row so that each girl is between two boys is

A group consists of 7 boys and 5 girls . Find the number of ways in which a team of 5 members can be selected so as to have atleast one boy and girl.

If m>n , the number of ways m men and n women can be seated in a row, so that no two women sit together is