QuestionsCategory: Business MathematicsPermutation and Combination
Harit Thakuri Staff asked 2 months ago

In how many ways 4 boys and 6 girls be seated in a line so that no two boys may sit the even place?

To ensure that no two boys sit at even places, we can arrange the girls and boys alternatively, and then arrange the boys in the remaining positions.

Let's denote G as a girl and B as a boy. The pattern will be GBGBGBGBGB, where G represents a girl, and B represents a boy. There are 5 positions for boys in this pattern.

Now, we need to place the 4 boys in these 5 positions. We can choose 4 positions out of 5 for the boys in (5P4) ways.

Once the positions for the boys are selected, we can arrange the boys among themselves in those positions in 4! ways.

The girls can be arranged in the remaining positions in 6! ways.

So, the total number of ways to seat 4 boys and 6 girls in a line, ensuring no two boys sit at even places, is given by:(5P4)×4!×6! ways.

:) Happy Learning