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13 Jun 2017, 12:13
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gmat1011
First, we need to select the groups:
Since we have 8 people, the first team can be formed in 8C2 = (8 x 7)/2! = 28 ways. Since there are now 6 people left, the second team can be selected in 6C2 = (6 x 5)/2! = 15 ways. Since there are 4 people left, the third team can be selected in 4C2 = (4 x 3)/2! = 6 ways. Since there are 2 people left, the final team can be selected in 2C2 = 1 way.
Thus, the total number of ways to select the 4 teams is 28 x 15 x 6 x 1 = 2520, if the order of selecting these teams matters. However, the order of selection doesn’t matter, so we have to divide by 4! = 24. Thus, the total number of ways to select the teams when order doesn’t matter is 2520/24 = 105.
Answer: E
10 Dec 2017, 11:06
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Balvinder
Let the 8 people be: A, B, C, D, E, F, G, and H
Take the task of creating the teams and break it into stages.
Stage 1: Select a partner for person A
There are 7 people to choose from, so we can complete stage 1 in 7 ways
ASIDE: There are now 6 people remaining. Each time we pair up two people (as we did in stage 1), we'll next focus on the remaining person who comes first ALPHABETICALLY.
For example, if we paired A with B in stage 1, the remaining people would be C, D, E, F, G and H. So, in the next stage, we'd find a partner for person C.
Likewise, if we paired A with E in stage 1, the remaining people would be B, C, D, F, G and H. So, in the next stage, we'd find a partner for person B.
And so on...
Stage 2: Select a partner for the remaining person who comes first ALPHABETICALLY
There are 5 people remaining, so we can complete this stage in 5 ways.
Stage 3: Select a partner for the remaining person who comes first ALPHABETICALLY
There are 3 people remaining, so we can complete this stage in 3 ways.
Stage 4: Select a partner for the remaining person who comes first ALPHABETICALLY
There is 1 person remaining, so we can complete this stage in 1 way.
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create 4 pairings) in (7)(5)(3)(1) ways (= 105 ways)
Answer: E
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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13 Oct 2018, 17:59
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saurabhgoel
The first team can be selected in 8C2 = (8 x 7)/2! = 28 ways.
The next team can be selected in 6C2 = (6 x 5)/2! = 15 ways.
The next team can be selected in 4C2 = (4 x 3)/2! = 6 ways.
The final team can be selected in 2C2 = 1 way.
However, since ORDER OF THE TEAMS DOES NOT MATTER, we need to divide the total number of ways to select the teams by 4! since we have 4 different teams. So we have:
(28 x 15 x 6)/4! = 2520/24 = 105
Answer: E
