Question

n how many different ways can i collect a total of 20 dollars from 4 different childrenand 3 different adults if each child can contribute up to 6 dollars and each adult cangive up to 10 dollars? (we assume that everyone gives a nonnegative whole number ofdollars).

Answer 1

To find the number of different ways to collect a total of $20 from 4 children and 3 adults, you need to consider the different combinations of how much each person can contribute. There are 24 ways in total to achieve this.

Step-by-step explanation:

To find the number of different ways to collect a total of $20 from 4 children and 3 adults, we need to consider the different combinations of how much each person can contribute.

Let's start with the children. Each child can contribute up to $6, so we can have the following possibilities:

1. All 4 children contribute $0: There is 1 way to achieve this.
2. 3 children contribute $0 and 1 child contributes $20: There are 4 ways to achieve this (one for each child).
3. 2 children contribute $0 and 2 children contribute $20: There are 6 ways to achieve this (we choose 2 children out of 4 that will contribute $20).
4. 2 children contribute $6 and 2 children contribute $8: There are 6 ways to achieve this (we choose 2 children out of 4 that will contribute $8).
5. 1 child contributes $0, 2 children contribute $6, and 1 child contributes $8: There are 12 ways to achieve this (we choose 1 child out of 4 that will contribute $0 and 2 children out of 3 that will contribute $6).
6. All 4 children contribute $6: There is 1 way to achieve this.

Now let's move on to the adults. Each adult can contribute up to $10:

1. All 3 adults contribute $0: There is 1 way to achieve this.
2. 2 adults contribute $0 and 1 adult contributes $20: There are 3 ways to achieve this (one for each adult).
3. 1 adult contributes $0 and 2 adults contribute $20: There are 3 ways to achieve this (we choose 1 adult out of 3 that will contribute $0).
4. All 3 adults contribute $20: There is 1 way to achieve this.

To calculate the total number of ways, we need to multiply the number of possibilities from the children and the adults. In this case, we have 24 ways to collect a total of $20 from 4 children and 3 adults.