If there are 7 class periods in a school day, and a typical student takes 4 classes, how many different time patterns are possible for the student?
A)70
B)105
C)33
D)32
E)35

Question

Quizplus · Accepted Answer

The number of different time patterns for the student can be calculated using the combination formula, which is used to find the number of ways to choose a subset of items from a larger set, without regard to the order of the items in the subset. The formula for combinations is C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and "!" denotes factorial, the product of all positive integers up to that number.Here, n = 7 (the total number of class periods) and k = 4 (the number of classes a student takes). Thus, the number of different time patterns is C(7, 4) = 7! / [4!(7-4)!] = (7*6*5) / (3*2*1) = 35.

If There Are 7 Class Periods in a School Day