Question

Five persons including three women sit in row to match a movie ,then the number of

ways in which the arrangements can be done , so that the women do not occupy the end

seats is …​

Answer 1

Answer:

4 is the answer..............

Answer 2

Given:

Number of people watching  the movie = 8(5 persons + 3 women)

To find:

We are asked to find the number of arrangements that can be made so that the women do not occupy the end seats

Solution:

As the question says that women should not occupy the end seats,let us first arrange the men.

So from the five persons 2 are selected to arrange in end seats in ⁵C₂ ways

                     M _ _ _ _ _ _M

Now the arrangement of 2 selected men can be done in  ⁵C₂ ×2! ways

Now there are 3 men and 3 women left over to be arranged,they can be arranged in 6! ways.

Total number of arrangements =  ⁵C₂ ×2!×6! = 14400

∴The total number of arrangements that can be made so that women donot occupy end seats = 14400