A group of 6 is formed. People are chosen from 5 kids, 8 teachers, 5 principals, 10 parents, 4 professors and 6 adults. If it's random, what's the probability that there is one person from each group?

Answer 1

The total number of ways you can make the right mix is 5 x 8 x 5 x 10 x 4 X 6.

The total number of different combinations possible is the combination of 38 people 6 at a time or

38!/(6!32!)

Divide the number of ways you can get the right mix by the total number of possible combinations: that's your probability.

Another way to do this is counting: The probability of picking the first group is 5/38, next is 8/37, 5/36, etc.. The product of these will be the probability of picking the right people in that order. We need to multiply by 6! because we can pick these people in any order and their are 6! orders of the 6 categories.

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