probability again (how many groups of at least 2 people...)

[thelazyman]

Hi, the question asks.

How many groups consisting of at least 2 people can be chosen from a group of 10 people?

I tried...

10!/2!2!2!2!2! Thinking that 5 groups can be formed but got the wrong answer.

 

[pka]

Re: probability again

How many groups consisting of at least 2 people can be chosen from a group of 10 people?

I am not doing this completely. Here are hints.
‘Groups’ in this context are subsets!
If there are N elements in a set, then there are 2<SUP>N</SUP> subsets of that set.
Now one of those sets is the empty set - the null-group no members.
There are N singletons set, subsets with only one element.
Now you combine those along with what you learned from the dice problem and finish it this off. Post your answer and we will check it.

 

[Guest]

is it 2^10 - 10?

 

[pka]

is it 2^10 - 10?

Actually it is \(\displaystyle \L
2^{10} - 11\)

Think about why 11!

 

[Guest]

total - 1 - 0
2^10 -10 -1

cool, thanks