Question

A jar contains 4 red marbles, 3 green marbles, 2 white marbles, and 1 purple marble. You randomly grab 5 marbles. Of the groups of the selected 5 marbles, how many will have at least one white marble?

Answer 1

126

Explanation:

To calculate this, we need to assume at least one white marble will be picked... so let's take it out of the bag. Then we need to pick 4 more marbles... it's just then a combination calculation.

How many marbles is there in total? 4 + 3 + 2 + 1 = 10

We do just as if we had removed one white marble from the bag... so that leaves 9 in the bag.

We have to pick 4 out of those 9.... so, it's simple combination calculation:

C(9,4) = 9! / (4! (9--4)!) = 9! / (4! 5!) = 126

Some of those grabs will have 2 white marbles... but we're assured that there are 126 ways to combine the 10 marbles so there's at least one white in the 5 picked (since we forced it in our calculations).