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A bag of Candy contains yellow, orange and brown colored pieces (each candy is one solid...

A bag of Candy contains yellow, orange and brown colored pieces (each candy is one solid color). There is plenty of each color in the bag. a. If we reach in and grab a handful of ten candies, how many different color combinations are possible? Keep in mind that candies of the same color are considered identical. b. How many ten candy combinations are possible where at least one of each color is drawn? c. Suppose we instead draw candies one at a time from the bag. How many candies must we draw to ensure that we obtain at least five of each color?

Math   Statistics-And-Probability   
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Answer #1

a) The number of combinations for 10 candies where same colour candy is considered identical is computed using the multinomial formula as:

a + b + c = 10

Number of solutions:

Therefore there are 66 solutions possible here.

b) As we are to draw at least one candy of each colour, the number of possible combinations here is computed using the multinomial formula as:

Therefore there are 36 possible combinations here.

c) As there are unlimited candies of each colour, we cannot really ensure the number of candies drawn such that we get one candy of each colour, this is because in 1 case out of the infinite case possible, there is also a possibility that we keep drawing the same colour candy ( This could have had an answer if there were limited number of candies of each colour )

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