A rowing crew of 4 rowers is to be selected, in order from the first seat to the fourth seat,
from 8 candidates. How many different arrangements are possible if:
a) there are no restrictions?
b) Jason or Kris must row in the first seat?
c) Jason must be in the crew, but he can row anywhere in the boat?
a) There are 8 choices for the first seat, then 7 choices for the second seat (since one person has already been chosen), then 6 choices for the third seat, and finally 5 choices for the fourth seat. Therefore, the total number of arrangements is:
8 × 7 × 6 × 5 = 1,680
b) There are 2 choices for who can row in the first seat (Jason or Kris), then 7 choices for the second seat (since one person has already been chosen), 6 choices for the third seat, and 5 choices for the fourth seat. Therefore, the total number of arrangements is:
(2 × 7 × 6 × 5) = 420
c) Jason must be one of the rowers and there are 7 choices for which of the remaining candidates will take the first seat. Once the first seat is selected, there are 7 remaining candidates for the second seat, 6 for the third seat, and 5 for the fourth seat. Therefore, the total number of arrangements is:
7 × 7 × 6 × 5 = 1,470