Discrete Math Exercise Many ways are there for 8 men and 5 w

Discrete Math

Exercise: Many ways are there for 8 men and 5 women to stand in a line so that no two women stand next to each other What is the answer if there are 10 men and 6 women? What is the answer if there are m men and w women with m w?

Solution

let 8 ment stand in line , so available position for women to stand are 9

total number of ways = 8P8 * 9P5 = 609638400

b)

total number of ways = 10P10 * 11P6 = 1207084032000

c)

total number of ways = mPm * (m+1)Pw