Each of five people randomly chooses one of five calculus sections to take (A, B, C, D, or E).
(a) What is the probability that they all choose the same one?
(b) What is the probability that they each choose a different section?
(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: [tex]\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}=\frac{1}{3125}[/tex]
(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: [tex]\frac{5!}{5^{5}}=\frac{24}{625}\ or\ 0.0384[/tex]
