Problem Solving

In how many arrangements can a teacher seat 3 girls and 3 boys in a row of 6 seats if the boys are to have the first, third, and fifth seats?

a. 6
b. 9
c. 12
d. 36
e. 720

answer is D

The number of arrangements of the seats is (# of possible choices for seat 1)(# of possible choices for seat 2)...(# of possible choices for seat 6).

There are 3 choices for the first seat since there are 3 boys. With that seat covered, there are 2 choices for the third seat. Likewise, there are is only one choice for the fifth seat.

Similarly, since there are 3 girls, we have 3 choices for the second seat, 2 choices for the fourth seat, and 1 choice for the sixth seat.

So the number of seat arrangements is 3*3*2*2*1*1 = 9*4 = 36

for such problems permutation formulae really help. I usually do it as follows:
3 boys can be arranged in hte 1st 3rd and 5th seat in 3! ways and 3 girls in the remaining seats as 3! ways so total ways is 3!*3! = 36.

Thank you