Question

A business has 5 labeled bins for 5 different charities. You

have 10 identical cans of soup. How many different ways can you
donate your soup to the different charities?

Answer 1

To find the number of different ways to donate the soup to the different charities, we can use the concept of combinations. There are 5 labeled bins and 10 identical cans of soup, so we need to find the number of ways to choose 10 cans to donate among the 5 bins. Using the formula for combinations, we calculate that there are 252 different ways to donate the soup.

Step-by-step explanation:

To find the number of different ways to donate the soup to the different charities, we can use the concept of combinations. Since there are 5 labeled bins and 10 identical cans of soup, we need to find the number of ways to choose 10 cans to donate among the 5 bins.

We can use the formula for combinations to calculate this. The formula for combinations is given by:

C(n, r) = n! / (r! * (n-r)!)

Where n is the total number of items to choose from (10 cans) and r is the number of items to choose (5 bins). Plugging in the values, we have:

C(10, 5) = 10! / (5! * (10-5)!)

Simplifying further:

C(10, 5) = 10! / (5! * 5!)

Using factorials:

C(10, 5) = (10 * 9 * 8 * 7 * 6 * 5!) / (5! * 5!)

The factorials in the numerator and denominator cancel out:

C(10, 5) = 10 * 9 * 8 * 7 * 6 / (5 * 4 * 3 * 2 * 1)

Simplifying further:

C(10, 5) = 252

So, there are 252 different ways to donate the 10 cans of soup to the 5 different charities.