Use a binomial to solve this, because order does not matter (i.e., if person #3 get's picked first or picked last, it doesn't matter)
Binomial Formula:
n choose k = n! / [ (n-k)! k! ]
Plug in the Numbers and Solve:
I'll include some of the math steps, so you can see how things cancel out nicely to be able to do these in your head.
8 choose 4 = 8! / [ (8-4)! 4! ]
8! / ( 4! x 4! )
(8 x 7 x 6 x 5 x 4 x 3 x 2) / ( 4 x 3 x 2 x 4 x 3 x 2 )
(8 x 7 x 6 x 5) / (8 x 3)
(7 x 6 x 5) / 3 = (7 x 2 x 5) = 70 combinations
The answer is 70 combinations.
4
There are 8!/(4!*4!) = 70 ways.
-5
3 people can be selected from a pool of 7 people in (7 x 6 x 5) = 210 ways.But each group of 3 can be selected and seated in (3 x 2 x 1) = 6 ways.So the number of different 3-person subcommittees formed from 7 people is (210/6) = 35 .
-6
-1
4
There are 8!/(4!*4!) = 70 ways.
Nine people can be selected from the group in(12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4) = 79,833,600ways.But each group of the same 9 people can be selected in(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2) = 362,880 different orders.So the number of different 9-person committees that can be selected is79,833,600/362,880 = 220 .
Typically a group of people selected from within a corporation that will work together in a committee to make an event happen. this will include budgeting, promoting and scheduling along with many other functions.
-5
5 for 2, 3 for 3, 2 for 4.
30240
There is no specific number of vultures in a committee. A committee of vultures is just a group of vultures.
4 people can be selected from a pool of 15 people in (15 x 14 x 13 x 12) = 32,760 ways.But each group of 4 can be selected and seated in (4 x 3 x 2 x 1) = 24 ways.So the number of different 4-person subcommittees formed from 15 people is (32,760 / 4) = 8,190 .
Nine people can be selected from the group of 12 in(12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4) = 79,833,600ways.But each group of the same 9 people can be selected in(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2) = 362,880 different orders.So the number of different 9-person committees that can be selected is79,833,600/362,880 = 220 .
3 people can be selected from a pool of 7 people in (7 x 6 x 5) = 210 ways.But each group of 3 can be selected and seated in (3 x 2 x 1) = 6 ways.So the number of different 3-person subcommittees formed from 7 people is (210/6) = 35 .