3 boys and 3 girls go to the theatre, and there are 2 seats in the front row. How many different ways can the friends be seated if a boy sits on the left?

Question

This is an arrangements and restrictions problem but I don't know how to do the correct steps.

Answer 1

Rather poor problem...not enough seats for the six. What is supposed to happen--four people leave, asking for a refund, or are there numerous other seats available, and in that case, what is the scope of seating options?

Answer 2

For the seat on the left, we have 3 options, choose 1. For the seat on the right, we have 5 remaining options, choose 1. So, we have 3 * 5 = 15 arrangements of two people seated, with a boy on the left. As Kenneth mentioned, it's sad for the other four who are left out.

 

Let's check by calling the boys A, B, and C and the girls X, Y, and Z. The possible arrangements are:

AB AC AX AY AZ BA BC BX BY BZ CA CB CX CY CZ

There are 15.