Question

A cafe owner sells 10 different types of sandwiches. Hassan buys a different type of sandwich on Monday, on Tuesday, and on Wednesday. In how many ways can he do this?

A) 10 ways
B) 30 ways
C) 720 ways
D) 1000 ways

Answer 1

Hassan has 10 choices on Monday, 9 on Tuesday, and 8 on Wednesday. Multiplying these numbers gives us 720 different ways he can choose a sandwich over the three days. Option C.

Step-by-step explanation:

The student's question is a classic example of a permutation where the order in which the sandwiches are chosen matters. As the cafe owner sells 10 different types of sandwiches, Hassan has 10 choices on Monday.

After picking one on Monday, there are 9 choices left for Tuesday. Then for Wednesday, he has 8 choices. Therefore, the total number of ways Hassan can choose a different sandwich each day for three days is 10 × 9 × 8 = 720 ways. Option C.