Answer to Question #245921 in Statistics and Probability for anonymous456

Question

There are 10 men and 10 women. Alice (woman) and Brad (man) never stand next to each other.

Assume that the men and women alternate in a line, how many possible ways are there for the

arrangement?

Answer 1

If started with man the arrangement is $*W*W*W*W*W*W*W*W*W*W$

Possible ways arranging the 10 women are = 1O!

There are 11 places for 10 men possible arrangements for men's are = 11P₁₀

Total arrangements are = $10!*11P_{10}$

If we stared with either man and women 2 ways also

Hence total arrangements are = $2*10!*11P_{10}$ ways or

$=2*3628800*39916800\\ =289700167680000 \space ways$