7. The manager of the soda shop decides that because you are a good customer, you may use a flavor as many times as you'd like. How many different possible mixtures can you make now (remember, you have 13 flavors available to you and you must choose 6?

The different possible mixtures can you make is 1716.

Step-by-step explanation:

Given that,

The total number of flavors available in the shop = 13 flavors The number of flavors you need to choose = 6 flavors

Here, we have to use the formula for combination,

nCr = n! / r! * (n-r) !

where,

n is the total number of flavors r is the number of flavors you need to choose

⇒ 13C6 = 13! / 6! * (13-6) !

⇒ 13! / (6! * 7!)

⇒ 13 * 12 * 11 * 10 * 9 * 8 * 7! / (6! * 7!)

⇒ 13 * 12 * 11 * 10 * 9 * 8 / 6!

⇒ 13 * 12 * 11 * 10 * 9 * 8 / 6 * 5 * 4 * 3 * 2 * 1

⇒ 1716

Therefore, you can 1716 different possible mixtures.