SOLUTION: There are 16 girls and 20 boys in a class. A team of 3 students is to be selected for preparing a science project from this class. How many ways can a two boys and a girl be select
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Question 1172653: There are 16 girls and 20 boys in a class. A team of 3 students is to be selected for preparing a science project from this class. How many ways can a two boys and a girl be selected from this class?
For this question, I’m assuming we need to use permutations since order counts (one girl, 2 boys). I have tried 36 and 3 because 16 plus 20 is 36. I’m having trouble coming up with the right solution. Answer by ikleyn(52781) (Show Source):
It is your mistake to think that the order does matter in this problem.
It DOES NOT: the team (John,Martha,Peter) is THE SAME as the team (Peter,John,Martha).
Therefore, you should use COMBINATIONS.
You can select 2 different boys from 20 boys by = = 10*19 = 190 different ways.
You can select one girl from 16 girls by = 16 different ways.
Since the selections in different (disjoint) categories are independent, the total number of different teams is the product
. = 190*16 = 3040. ANSWER
Solved.
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