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Question

What is the number of distinct 4-person committees that can be chosen from a group of 6 people?

I know I asked this question earlier, but can someone explain the steps to me?

Answer 1

I seem to remember that this is given by:-
6 ! / (2 ! 4 !)
= (6) (5) / 2
= 15

Answer 2

Fifteen.
If you name the people A, B, C, D, E, and F, you can have:

1. ABCD
2. ABCE
3. ABCF
4. ABDE
5. ABDF
6. ABEF
7. ACDE
8. ACDF
9. ACEF
10. ADEF
11. BCDE
12. BCDF
13. BCEF
14. BDEF
15. CDEF

I started with ABCD, then changed the last person to E, then to F. Then I backed up to the third person and changed them to D, but I didn't start with ABDD, because that would have put the same person on the committee twice, and I didn't go back to ABDC, because that's just a rearrangement of ABCD. I just proceeded from there, replacing members of the committee until I'd included them all.

Not very algebraic, I know, but it works. If you want to do it algebraically, you have to use the equation for the number of combinations possible from a set.

C = [n(n-1)(n-2)(n-3)... to k factors] / k!

Where n is the number of people available (6 in this case) and k is the number of people in each committee (4). k! is k factorial, or the number you get when you multiply all the whole numbers between 1 and k. For example, if k = 4, then:
k! = 4! = 1 x 2 x 3 x 4 = 24

So the total number of combinations is:

C = [(6)(6-1)(6-2)(6-3)] / 24
C = [(6)(5)(4)(3)] / 24
C = 360 / 24
C = 15

There ya go.

Answer 3

You can simplify this by saying that choosing 4 to go on the committee is the same as choosing 2 to be left out.

The first person can be chosen in 6 ways.
The second person can be chosen in 5 ways.
That gives 30 possibilities, but they will not all be different, as you could have chosen first A and then B, or first B and then A in every case.
Divide the 30 by 2 to get 15 as the answer.

In formal notation that is 6C4 or C(6,4)
= 6! / ( 2! 4! )
= 6 * 5 / 2
= 15.

Answer 4

To calculate the number of ways to choose r of n objects, without repetition, use the formula (n!)/r!(n-r)!

In your example: 6!/2!(6-2)! = 1*2*3*4*5*6/1*2*(1*2*3*4)
= 5*6/2 = 15

ADDENDUM

robertonereo missed
1345
1346
1356
1456
2456

Answer 5

I HATE ALGEBRA! im in 8th grade and already in algebra 2 that's hilarious because of the fact i didnt even comprehend algebra I or maybe pre algebra. it doesnt make any experience to me and its sooo pointless no ones even gonna use this in every day existence heavily, i failed it each grading quarter even although i stayed after class plenty and that i've got been given help particularly much every day

Answer 6

Persons = 1 2 3 4 5 6
You may have:
1) 1234
2) 1235
3) 1236
4) 1245
5) 1246
6) 1256
7) 2345
8) 2346
9) 2356
10) 3456

10 distinct committees

Answer 7

Thats 6C4=15