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08 Oct 2022, 02:40
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D
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Difficulty:
75%
(hard)
Question Stats:
34% (00:57) correct
66%
(01:04)
wrong
based on 152
sessions
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6 members are to be divided into two groups of 3 members each. In how many ways this can be done?
A. 120
B. 60
C. 20
D. 10
E. 2
A. 120
B. 60
C. 20
D. 10
E. 2
08 Oct 2022, 11:12
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The members can be distributed as follows:
6*5*4 and 3*2*1
Now, since this approach counts different arrangements of the same 3 people in each group, which isn't warranted by the question, each group has to be divided by
3! = 6
So the first group has 6*5*4/6 = 20 and the second group 3*2*1/6 = 1
A key point is whether there is a functional difference between the two groups.
If so, we're done and the total ways equals
20*1 = 20
If there is no functional difference between the two groups, as is the case here because the question makes no mention of this, then since the same 3 people can appear in each group, the number of arrangements previously calculated, 20, should be divided by 2, yielding
10 ways
Posted from my mobile device
6*5*4 and 3*2*1
Now, since this approach counts different arrangements of the same 3 people in each group, which isn't warranted by the question, each group has to be divided by
3! = 6
So the first group has 6*5*4/6 = 20 and the second group 3*2*1/6 = 1
A key point is whether there is a functional difference between the two groups.
If so, we're done and the total ways equals
20*1 = 20
If there is no functional difference between the two groups, as is the case here because the question makes no mention of this, then since the same 3 people can appear in each group, the number of arrangements previously calculated, 20, should be divided by 2, yielding
10 ways
Posted from my mobile device
rajtare
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08 Oct 2022, 15:41
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Snehaaaaa
Let 6 people be a,b,c,d,e,f
if there is no restriction these 6 people can be distributed in 6c3*3c3 = 20
now look at the groups
abc, def
abd,cef
abe,cdf
abf,cde
acd,bef
ace, bdf
acf,bde
ade,bcf
adf, bce
aef, bcd
now the other 10 groups are just the arrangement of above 10 groups, i.e abc = bac =cab. hence we have to divide the total number of ways by 2 to get the final answer = 20/2 =10
Additionally.
This question can be solved by using distribution formula. please follow the link for the same. https://gmatclub.com/forum/topic215915.html#p1667366
6!/((3!)^2*2!)
= 10
