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Re: Problem solving - 3 groups of 3 [#permalink]
19 Jul 2011, 11:10
Think of it like an experiment: 1. Select 3 people from 9 at random 2. Select another 3 people from the 6 remaining people 3. Select another 3 people for the 3 remaining people
The first thing to notice is that steps 1 and 2 completely determine step 3. The second thing to notice is that since we're selecting teams, order doesn't matter, so we should use combinations 9C3 = (9*8*7)/(3*2*1) =168 6C3 = (6*5*4)/(3*2*1) = 20
By the fundamental counting principle, we should multiply these two numbers to see how many outcomes our experiment has 168*20 = 3,460
Re: Problem solving - 3 groups of 3 [#permalink]
19 Jul 2011, 12:23
Solution: The first group 9C3=84 The second group 6C3=20 And the last group 3C3=1 In total have 84∙20∙1=1680 ways, but, exist repetitions in ways, then: ( 9C3∙ 6C3∙ 3C3)/3!=1680/6=280
Second, 1/3rd of the combinations will be repetitions in 3 groups of 3 and 1/2 of the combinations will be repetitions in 2 groups of 3. So you should divided the result be 3 and 2 respectively arriving at 280.
Re: Problem solving - 3 groups of 3 [#permalink]
22 Jul 2011, 17:45
There are multiple ways to solve this question.
1. Anagram: Let's focus on how to use this method, so that you can reuse it. Solution: = 9!/ (3!*3!*3!) = 1680
2. Direct and more reliable solution is to just visualize one person at a time. Solution: = (ways to select 3 out of 9) * (ways to select 3 our of remaining 6) * (ways to select 3 out of remaining 3) = 9C3*6C3*3C3 = [9!/(6!*3!)] *[6!/(3!*3!)]*1 = 9!/(3!*3!*3!) = 1680
Ans: "C"
---------------------------------------------------------- I made a mistake early on. I assumed they are 3 distinct group and hence thought order mattered. But this is NOT indicated in the question and MY ASSUMPTION WAS WRONG!
Hence the ans needs to divided by 3! (the number of ways the 3 groups can be rearranged). Hence 1680/3!=280. Ans: A
Thanks manishgeorge for pointing it out.
Hope this helps!
Last edited by abhicoolmax on 22 Jul 2011, 18:58, edited 2 times in total.
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