Question

In the cafeteria there are seven different snack options, you can only have up to three snacks and you can't have multiple of the same options. How many different snack combos are possible?

(Hint, you can have just one or two snacks but no more than three)

Answer 1

Answer: There are 64 different snack combinations possible when you can choose up to three snacks from seven different options without having multiple of the same options.

Explanation:

To find the number of different snack combinations when you have seven different options and can choose up to three snacks without having multiple of the same options, you can use combinations.

You're essentially finding the number of ways to choose 0, 1, 2, or 3 snacks from 7 options. You can calculate this by summing the combinations for each possibility:

Combinations of choosing 0 snacks from 7 options: C(7, 0) = 1 combination

Combinations of choosing 1 snack from 7 options: C(7, 1) = 7 combinations

Combinations of choosing 2 snacks from 7 options: C(7, 2) = 21 combinations

Combinations of choosing 3 snacks from 7 options: C(7, 3) = 35 combinations

Now, add them up:

1 + 7 + 21 + 35 = 64

There are 64 different snack combinations possible when you can choose up to three snacks from seven different options without having multiple of the same options.