Question

Each of five people randomly chooses one of five calculus sections to take (A, B, C, D, or E).

Answer 1

(a) The probability of choosing a specific section is 1/5 on each choice. Therefore the probability they all choose the same one is given by:
$\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}=\frac{1}{3125}$

(b) There are 5! permutations of the 5 sections without repetitions and there are  5^5 permutations with repetitions. Therefore the probability they each choose a different section is given by:
$\frac{5!}{5^{5}}=\frac{24}{625}\ or\ 0.0384$