Question

Suppose there are (n) students at Michigan and (k) clubs. Every student may join any number of clubs, possibly zero. Let (s) be the number of ways in which students can join clubs. The value of (s) is:

a) (2^n)
b) (n^k)
c) (k^n)
d) (2^nk)

Answer 1

The number of ways in which students can join clubs is 2^n.

Step-by-step explanation:

The number of ways in which students can join clubs can be determined using the concept of combinations. Since each student can join any number of clubs, possibly zero, the total number of ways can be found by adding up the possibilities for each student. For each student, there are 2 possibilities - either they join a club or they don't. Therefore, the total number of ways is 2^n, which is option (a).