Consider a bag of jelly beans that has 30 red 30 yellow and

Consider a bag of jelly beans that has 30 red, 30 yellow, and 30 green jelly beans.


a)  How many color sequences can you get by drawing 6 beans from the bag?

b) How many color combinations of 10 beans have exactly two yellow beans?

c) How many color combinations of 10 beans have at most two yellow beans?

Solution

a)

There are 3 colors for each draw.

Thus, there are 3^6 = 729 sequences. [ANSWER]

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b)

There are 10C2 ways to choose the position of the 2 yellow beans.

The other 8 beans can be chosen in 2^8 ways.

Thus, there are

2^8 (10C2) = 11520 [ANSWER]

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c)

For 1 yellow bean:

There are 10C1 ways to choose the position of the 1 yellow bean.

The other 9 beans can be chosen in 2^9 ways.

For the 0 yellow beans:

There are 10C0 ways to choose the position of the 0 yellow beans.

The other 10 beans can be chosen in 2^10 ways.

Thus, the total number of ways is

2^8 (10C2) + 2^9 (10C1) + 2^10 (10C0) = 17664 [ANSWER]