Question

Carla selects 5 fruit-flavored candies from a bowl containing 6 apple, 5 banana and 4 cherry candies. How many possible combinations of candies can Carla select

Answer 1

To find the number of possible combinations of candies, use the formula for combinations: C(n, k) = n! / (k! * (n - k)!). In this case, there are 3,003 possible combinations of candies that Carla can select.

Step-by-step explanation:

To find the number of possible combinations of candies, we need to use the concept of combinations. A combination is a way to select items from a larger set without regard to the order in which they are selected.

In this case, Carla is selecting 5 fruit-flavored candies from a bowl containing 6 apple candies, 5 banana candies, and 4 cherry candies. To find the number of possible combinations, you can use the formula for combinations:

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

where n is the total number of items and k is the number of items being selected.

Substituting the values into the formula, we have:

C(15, 5) = 15! / (5! * (15 - 5)!)

= 3003

Therefore, there are 3,003 possible combinations of candies that Carla can select from the bowl.

Answer 2

Carla can select from 3,003 possible combinations of 5 candies from a bowl containing 6 apple, 5 banana, and 4 cherry candies.

To determine how many possible combinations of candies Carla can select from the bowl containing 6 apple, 5 banana, and 4 cherry candies, we can use combinatorial mathematics. As she selects 5 candies, the order doesn't matter and replacement is not allowed, so we need to calculate combinations.

Step-by-Step Solution:

1. First, we calculate the total number of candies: 6 apple + 5 banana + 4 cherry = 15.
2. Since the order of selection doesn't matter, we use the combination formula: C(n, k) = n! / (k!(n-k)!), where 'n' is the total number of items, 'k' is the number of items to choose, and '!' denotes factorial.
3. So, we need to find C(15, 5) to determine the number of ways she can select 5 candies.
4. Calculating this, we get C(15, 5) = 15! / (5!(15-5)!) = 15! / (5!10!) = 3,003

Since the order of selection doesn't matter, we use the combination formula: C(n, k) = n! / (k!(n-k)!), where 'n' is the total number of items, 'k' is the number of items to choose, and '!' denotes factorial.

Calculating this, we get C(15, 5) = 15! / (5!(15-5)!) = 15! / (5!10!) = 3,003.

Therefore, Carla has 3,003 possible combinations of candies when selecting 5 from a assortment of 6 apple, 5 banana, and 4 cherry candies.