SOLUTION: You volunteer to help drive children at a charity event to the​ zoo, but you can fit only 6 of the 16 children present in your van. How many different groups of 6 children can yo

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Question 1201922: You volunteer to help drive children at a charity event to the​ zoo, but you can fit only 6 of the 16 children present in your van. How many different groups of 6 children can you​ drive?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
You volunteer to help drive children at a charity event to the​ zoo, but you can fit only 6 of the 16 children present in your van. How many different groups of 6 children can you​ drive?
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The 1st choice is 1 of 16.
Then 1 of 15, then 14, etc.
---> 16*15*14 ... 11
The product of those 6 numbers.
But, choosing A, B, C, D, E and F is the same as choosing A, F, C, etc.
6*5*4*3*2*1 different ways = 720 ways for any combination.
Divide the big number by 720.
That's it.
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.

ince the order of children in groups does not matter, this problem is on COMBINATIONS.


It asks how many different combinations of 6 children can be made of the group of 16 children.


The answer is   =  =  = 8008.

Solved, with explanations.

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On  Combinations,  see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.


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