Question

A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants.How many ways are there to choose 23 croissants with at least five chocolate croissants and at least three almond croissants?

Answer 1

Given data:

1. plain croissants

2. cherry croissants

3. chocolate croissants

4. almond croissants

5. apple croissants

6. brocolli

23 croissants must be chosen

8 are already chosen (at least 5 chocolate croissants and 3 almond croissants)

15 more to select out from the 6 types of croissants

Find: number of ways to select the remaining 15 croissants

Solution:

Selecting the types of croissants can be done in any order, hence, order doesn't matter here. We are dealing with combination.

`(6+15-1)C15=20C15=15,504`

Hence, there 15, 504 ways to choose 23 croissants with at least five chocolate croissants and at least three almond croissants.