A person makes 6 selections from a pool of 32, 1 through 32. Six balls are drawn from a pool of 32 without replacement. The probability of correctly matching all six balls drawn is 1 in C(32,6). The probability of correctly matching 5 of 6 balls is C(6,5) X C(24,1)/C32,6).
1. What is the probability that the person correctly matches 5 of the six balls drawn in any order and the first ball drawn (6 of 6 total)?
2. What is the probability that the person correctly matches 4 of the six balls drawn in any order and the first ball drawn (5 of 6 total)?
Thanks in advance for your help.