Blue Bag

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Frequently Asked Questions...

What is the answer to this probability question (10 points to 1st correct answer)?

Seven distinct pieces of candy are to be distributed among three bags. The red bag and the blue bag must each receive at least one piece of candy; the white bag may remain empty. How many arrangements are possible?
Please show all work. 10 points goes to first person to get it right.


Best Answer...

Answer:

Since both the candies & bags are distinct,
each candy has 3 choices of bag, so
unrestricted # of ways = 3^7 = 2187

It is permissible for the white bag to have no candies,
and the # of such arrangements are
R B WAYS
6 1 : 7c6 * 2! = 14
5 2 : 7c5 * 2! = 42
4 3 : 7c4 * 2! = 70
total : 126

But we have to subtract cases where
(a) 2 bags empty : 3c2 = 3
(b) 1 bag other than white is empty: 2*126 = 252

So finally, # of specified arrangements
= 2187 - 255
= 1932
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