MATH SOLVE

4 months ago

Q:
# Four married couples have reserved eight seats in a row at the theater. If they arrange themselves randomly, what is the probability that all the women will sit in adjacent seats and all the men will sit in adjacent seats?

Accepted Solution

A:

The required probability is 2.86%.Step-by-step explanation: The number of ways in which eight persons can sit within themselves at the reserved eight seats is given by[tex]N=8!.[/tex]And, the number of ways in which 4 couples (8 persons) can sit such that all the women will sit in adjacent seats and all the men will sit in adjacent seats is given by[tex]n=4!\times4!\times2!.[/tex]Therefore, the probability that all the women will sit in adjacent seats and all the men will sit in adjacent seats is[tex]p=\dfrac{n}{N}=\dfrac{4!\times4!\times2!}{8!}=\dfrac{4\times3\times2\times1\times4!\times2\times1}{8\times7\times6\times5\times4!}=\dfrac{1}{35}=2.86\%.[/tex]Thus, the required probability is 2.86%.