Question

from a group of six persons, how many committees of three can be formed if two of the six people cannont be on the same committee?

Answer 1

There are 6 people total, so you can form 6/3 = 2 committees of 3 people each

Two people can't be on the same committee. Call these two people person A and person B.

So let's say person A is on committee # 1, this means

Committee 1: A _ _

and you have 2 slots left and you have 6-2 = 4 people to fill those slots

So you have 4 C 2 = 6 ways to fill this committee

Answer 2

You then double this because you could easily have made person B part of committee # 1 (instead of person A)

Answer 3

ohhh so its 2(2C1)*4C2 ?

Answer 4

so I guess you could shorten it to

(2 C 1)*(4 C 2)

Answer 5

2 C 1 = 2, so no need for the extra 2 in front

Answer 6

i think that only makes out ot 12

Answer 7

There are (6c3)=20 committees possible. There are (4c1)*(2c2)=4 which include both of the 2 people and are subtracted. 20-4=16

Answer 8

dont i need the extra two in front cuz person A or person B

Answer 9

Yes there are 20 committees possible

But I think that there are (2 C 1)*(1 C 1)*(4 C 1) = 8 ways to have both A and B on the same committee

so there are 20 - 8 = 12 ways to have 2 committees where A and B are not on the same committee

Answer 10

oh LOLLLL wait the answer is 12 LOLLLL

Answer 11

yeah thought so

Answer 12

well there you have 2 ways to get there

Answer 13

haha dude thanks y'all ... god keep think its 16 so im like...

Answer 14

the way the question is worded, you are forming a single group of 3 at a time, not 2 groups of 3 at a time. that's where the difference is coming from.

Answer 15

well whatever you form of one group, the leftover people go into the second group

so it's the same thing really

Answer 16

but it doesn't matter if the 2 people are both in the 2nd group, because that group isn't the committee