Use the formula for nCr to solve Exercises 49–56.

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Question

Use the formula for nCr to solve Exercises 49–56.

You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?

Accepted Answer

Hey everyone here we are asked to find how many possible sets of two electives you can take if you have a total of 12 offered electives. So before we can solve this problem we first need to recall the combination formula which is n. C. R is equal to n factorial divided by the quantity of n minus R. Factorial times R factorial. And now in words this formula takes the number of possible combinations if our items are taken from n items. So in this case our our items are the two electives which we take from the total amount of electives so R is two and then our total number of items is N. So N is 12. And now with these values identified we can go ahead and plug them into our formula. So we have 12 C. Two is equal to in the numerator we have n factorial so we have 12 factorial. And in the denominator we have N which is 12 minus R, which is two quantity. And then we take the factorial of that quantity. And we also multiply it by R factorial which will be two factorial. And now we can work to work to make simplifications. So keeping the numerator the same for now we have factorial and then in the denominator we have 12 minus two which gives us 10 factorial times two factorial. And now since we have 10 factorial in the denominator we can expand the numerator just a bit. So we can also have 12 factorial in the numerator. So doing this in the numerator we will have 12 times 11 times 10 factorial. And again in the denominator we have 10 factorial times two factorial. But now we see that the 10 factorial in the numerator cancels out with the denominator. So we are left with 12 times 11 in the numerator and two factorial in the denominator is just two times one. So with this we have 12 times 11 which is 132 divided by two times one is just to simplifying 132 divided by two is simply 66. So we have found that we have 66 different possible combinations of two electives which we can take, which is answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time.

Use the formula for nCr to solve Exercises 49–56. You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?

Key Concepts

Combination (nCr)

Factorial

Counting Principles

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