Question

how many ways are there to choose 24 croissants with at least five chocolate croissants and at least three almond croissants?

Answer 1

To find the number of ways to choose 24 croissants with at least five chocolate croissants and at least three almond croissants, we need to consider different cases and calculate the number of ways for each case. This can be done by using combinations.

Step-by-step explanation:

To find the number of ways to choose 24 croissants with at least five chocolate croissants and at least three almond croissants, we need to consider the different cases.

1. Case 1: Selecting exactly 5 chocolate croissants and exactly 3 almond croissants. In this case, we choose 5 out of the remaining 19 non-chocolate croissants and 3 out of the remaining 14 non-almond croissants. The number of ways to do this is 19 choose 5 multiplied by 14 choose 3.
2. Case 2: Selecting more than 5 chocolate croissants and exactly 3 almond croissants. In this case, we choose 6 or more out of the remaining 19 non-chocolate croissants and 3 out of the remaining 14 non-almond croissants. We can calculate the number of ways for each value of chocolate croissants from 6 to 19 and sum up the results.
3. Case 3: Selecting exactly 5 chocolate croissants and more than 3 almond croissants. This is similar to Case 2, but with the roles of chocolate and almond croissants switched.
4. Case 4: Selecting more than 5 chocolate croissants and more than 3 almond croissants. Again, we calculate the number of ways for each value of chocolate and almond croissants and sum up the results.

By adding up the results from all four cases, we will get the total number of ways to choose the croissants.