Probability question Please show all details so that I may u

Probability question. Please show all details, so that I may understand the process. Thank you.

Question:

A conference room as m men and w women and m + w chairs.

a. Two of the men always sit together. Find the probability that all women are adjacent to each other.

b. Find the probability that no two women are adjacent to each other

Solution

a) for this literal you have m+w-2 posibilities for that all women sit adjacent to each other because 2 chairs will be for the 2 men that always sit together

and the favorable cases will be w because you have w women that need to sit together

so the probability will be = [(m+1)!w!]/(m+w)!

b)

as 2 men always sit together you will have m+w-2 chairs ( posibilities cases)

and you will have 2w for the women are adjacent to each other

so the probability that no 2 women are adjaent to each other will be

P= 1- [2W / M+W-2]