question i came across which confused me?

[nruthya.rajagopal]

the number of different subgroups that can be formed from 6 different item if each subgroup contain atleast 2 of these items.


i understand it is a combinatoric problem :
6!/(2!4!) if subgroups contain 2 items.
6 subgroups for 1 item
1 subgroup for no item.
15-6-1=8

Solution given is
2*2*2*2*2*2=64
64-6-1 =57


How is 2*2*2*2*2*2=64 and not 15?

[tommywallach]

Hey Nruthya,

I'm a little confused by the wording. In the future, please try to copy the text exactly, because small differences can make a question unrealistic, or downright insoluble.

But I assume the question is "How many groups can be made from 6 items, if each group must have at least 2 items in it"?

If so, the full solution would be wildly complicated, and not remotely realistic on the GRE. Where did you find this?

As for your final question, I definitely don't understand it.

2 * 2 = 4
2 * 2 * 2 = 8
2 * 2 * 2 * 2 = 16
2 * 2 * 2 * 2 * 2 = 32
2 * 2 * 2 * 2 * 2 * 2 = 64

I don't see where you'd get 15...

-t

[navigalactus]

lol Yes, I also couldn't get what he wants to know as the wording is ambiguous. He got 15 from 6C2.
The question that is posted cannot be understood

[tommywallach]

Glad we're agreed! But where's Nruthya?

-t