Use the formula for nCr to solve Exercises 49–56. Of 12 possib...

Question

Use the formula for nCr to solve Exercises 49–56. Of 12 possible books, you plan to take 4 with you on vacation. How many different collections of 4 books can you take?

Accepted Answer

Hey everyone here we are asked to find how many possible sets of four seeds we can plant when we have a total of 15 different seeds available. So before we can start solving this problem we need to recall the combination formula which is n. c. r is equal to and factorial. The divided by the quantity of n minus R. Factorial times R factorial. And now in words this formula is the number of possible combinations if our items are taken from n items. So with this in mind our items taken our our our our The groups of four, we want four seeds so our is four and then our total amount of seeds is going to be n. So we will have n equal to 15. And now with these values identified we can simply plug them into our formula and find our solution. So doing this we have 15 C. Four is equal to in the numerator instead of n factorial we have 15 factorial and in the denominator we have the quantity of n 15 minus R. Which is four factorial times R. Or four factorial. And now we can start making some simplification. So in the numerator will keep keep it as 15 factorial for now and in the denominator we have 15 -4 giving us factorial times four factorial. And now since we have this 11 factorial in the denominator we can expand the numerator until we have 11 factorial in the numerator as well. So doing this we have 15 times times 13 times 12 times 11 factorial. All divided by 11 factorial times four factorial. And with this we can clearly see that our 11 factorial is canceled out. And now we can simplify our expression and expand this four factorial in the denominator. So we have 15 times 14 times 13 times 12. All divided by four factorial which is four times three times two times one. And now from here we can see that we have a four times three in the denominator which is just 12. And we also have 12 in the numerator. So these terms cancel and we are left with times 14 times 13 in the numerator and in the denominator we just have two times one And now multiplying these terms together we have 2730 divided by two and dividing. We are left with our solution where we have a total possible number of combinations of 1,365 which is answer choice B 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. Of 12 possible books, you plan to take 4 with you on vacation. How many different collections of 4 books can you take?

Key Concepts

Combination Formula (nCr)

Factorials

Counting Without Replacement

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