Question

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?

Answer 1

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.