There are 4845 ways to choose 4 people out of 20
20 choose 4 = 20! / (4!16!)
There are 16C6 = 16*15*14*13*12*11/(6*5*4*3*2*1) possible committees. That is, 8,008 of them.
72
-5
I think there are 88 different combinations of coins that can make up 66 cents.
The number of distinct, different 4-person committees that can be formedfrom a group of 32 people is(32!/28!) / (4!) = (32 x 31 x 30 x 29) / (4 x 3 x 2 x 1) = 35,960(but obviously, no more than four at a time.)
120
To determine the number of different two-person committees that can be formed from a group of six people, we use the combination formula ( C(n, k) = \frac{n!}{k!(n-k)!} ), where ( n ) is the total number of people and ( k ) is the number of people to choose. Here, ( n = 6 ) and ( k = 2 ). Thus, the number of combinations is ( C(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15 ). Therefore, 15 different two-person committees can be formed.
Any combination of 5 students leaves one student out. Since there are 5 possible students to leave out, the number of combinations of all but one student is 5.
There are 16C6 = 16*15*14*13*12*11/(6*5*4*3*2*1) possible committees. That is, 8,008 of them.
Since the order doesn't matter, this is a combination problem.25C3 = 25*24*23/3*2*1 = 25*4*23 = 2300 committees.
They can't be split evenly into groups of six. Sixteen people can split into two groups of six, and there will be four people left over.
(9 x 8 x 7 x 6)/(4 x 3 x 2 x 1) = 126committees.
To determine how many 5-person committees can be formed from nine people, you can use the combination formula ( C(n, k) = \frac{n!}{k!(n-k)!} ), where ( n ) is the total number of people, and ( k ) is the number of people to choose. In this case, ( n = 9 ) and ( k = 5 ). Thus, the number of ways to select the committee is ( C(9, 5) = \frac{9!}{5!(9-5)!} = \frac{9!}{5!4!} = 126 ). Therefore, there are 126 different 5-person committees possible.
72
9 combinations - the key person and one of the remaining nine.
-5
There is no set number. It could be none at all.