Question

Sarah needs to go to five different stores. How many ways can she go to two of them before lunch?

Answer 1

Answer:

10

Step-by-step explanation:

Solution 1: At first, you might think that because there are 5 ways to choose the first store and 4 ways to choose the second store, the answer is 5 * 4 = 20 but this is over-counting by a factor of 2. Say that two of the stores are A and B. If she went to A then B, that's the same as going to B then A since you still go to the same stores, therefore, the answer is 20 / 2 = 10.

Solution 2: We need to find the number of ways to choose 2 stores from 5, we can do this by calculating ₅C₂ which equals:

5! / 2!  * 3!

= 5 * 4 * 3 * 2 * 1 / 2 * 1 * 3 * 2 * 1

= 5 * 4 / 2 * 1

= 10