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
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?
1 answer
1 answer