Adi_Pat wrote:Makes sense with the formula...Why is this approach giving me the wrong answer...
Number of ways of selecting 1 experienced person = 12
So that leaves 9 people....
Number of ways of selecting 2nd person = 9
Number of ways of selecting 3rd person = 8
Total number of ways = 12*9*8 = 864
Hi! You've worked out the problem as though order matters, which is why you got 72 instead of 36 for the second step (inexperienced) part of the question.
If the question had read:
3 seats in a canoe are going to be filled by 1 experienced person and 2 inexperienced people. There are 12 experienced canoeists and 9 inexperienced canoeists available. If the experienced canoeist must sit in the back and the inexperienced canoeists will occupy the first two seats, in how many ways can the 3 seats be filled?
then your solution would have been perfect. However, in the actual question we don't care about order, so you've double counted.
Let's call the inexperienced people A, B, C, D, E, F, G, H and I.
The way you've solved the problem, you could select A first and then B second; however, you could also select B first and then A second. You've counted these as 2 distinct selections, even though they're both simply A + B selected.
So, you need to divide by 2 to eliminate the double counting.
12 * (9 * 8)/2 = 12 * 72/2 = 12 * 36 = 432
