SOLUTION: You volunteer to help drive children at a charity event to the zoo, but you can fit only 6 of the 15 children present in your van. How many different groups of children can you
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Question 1169982: You volunteer to help drive children at a charity event to the zoo, but you can fit only 6 of the 15 children present in your van. How many different groups of children can you drive?
How many different groups of 6 children can you drive?
Found 2 solutions by math_tutor2020, Boreal:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
Consider 6 slots labeled A,B,C,D,E,F to represent the 6 people you select from the 15 total.
We have...
15 choices for slot A
14 choices for slot B
13 choices for slot C
12 choices for slot D
11 choices for slot E
10 choices for slot F
Note how I'm counting down one at a time. This is because once a student is selected, they can't be picked again.
Multiplying out those items gives us
15*14*13*12*11*10 = 3,603,600
which is the number of permutations.
If order mattered, then we'd stop here. However, order does not matter. Each seat is unlabeled and there is no ranking. All that matters is the overall group.
For any group of 6 people, there are 6! = 6*5*4*3*2*1 = 720 ways to arrange said group. We must divide the permutation count found above to get the answer we want.
number of combinations = (number of permutations)/720
number of combinations = (3,603,600)/720
number of combinations = 5,005
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We could also use the nCr combination formula
We have a pool size of n = 15 and r = 6 selections to make from that pool size.
!})
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This expression of (3,603,600)/720 shows up again
-------------------------------------------------
Answer: 5005
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is 15C6
=5005 different groups.
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