Mr. Greenberg has a class of 30 students. He is drawing names from a hat to determine first, second, and third prizes. How many ways can he pick the three students?

Question

a) 27,000 ways
b) 40,320 ways
c) 90 ways
d) 1,080 ways

Answer 1

Mr. Greenberg can first choose any of the 30 students for the first prize. After that, he can choose any of the remaining 29 students for the second prize, and any of the remaining 28 students for the third prize. Therefore, the total number of ways he can pick the three students is $30\times29\times28 = \boxed{\textbf{(b)}\ 40,320}$ ways.