A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
Choose the correct choice from the following choices:
A) 7! – 2!3!2! B) 7! – 4!3! C) 7! – 5!3! D) 7 × 2!3!2! E) 2!3!2!
7 people can be seated in 7! ways   take 3 men as one unit ----&gt; tot 5 people can be seated in 5 ways *(no. of ways in which 4 women can be seated amng themselves ) * ( no. of ways in which 3 men cen be seated amng themselves)=5*4!*3!=5!*3!   tot no. of ways in which 3 men are not seated in adjacent seats=tot arrangements - 5!*3!=7!-5!*3!   ANSWER:7! – 5!3!
<result>C</result>
A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?