A box of jelly bears contains 52 jelly bears which 19 are white, 10 are brown, 7 are pink, 3 are purple, 5 are yellow, 2 are orange, and 6 are green. In how many ways can you select 9 pieces of candy at random from the box without replacement if 3 white jelly bears are selected?
To solve this problem, we can use combinatorics and apply the concept of combinations.
First, we need to determine the number of ways to select 9 pieces of candy from the box without replacement. This is given by the formula C(n, r), where n represents the total number of candy bears in the box and r represents the number of candy bears we want to select.
In this case, there are a total of 52 candy bears in the box, so n = 52.
To calculate the number of ways to select 9 pieces of candy from these 52 without replacement, we can use C(52, 9).
However, we also need to consider that 3 white jelly bears are already selected. Therefore, we need to subtract the number of ways to select the remaining 6 candy bears from the remaining 49 bears in the box.
To calculate the number of ways to select 6 candy bears from these 49 without replacement, we can use C(49, 6).
Now we can calculate the total number of ways to select 9 pieces of candy, with 3 of the selections being white jelly bears:
C(52, 9) - C(49, 6)
Calculating this expression will give us the final answer.
Note: The notation C(n, r) represents the combination formula, which can be calculated using the formula C(n, r) = n! / (r! * (n - r)!). "!" denotes factorial, where n! = n * (n-1) * (n-2) * ... * 3 * 2 * 1.