In Exercises 9–16, use the formula for nCr to evaluate each expre...

Question

In Exercises 9–16, use the formula for nCr to evaluate each expression.

11C4

Accepted Answer

Hello. Today we are asked to evaluate the following combination. So the combination given to us is the combination of 13 and six. Now, in order to evaluate this, we need to understand the general combination. The general combination is given to us as the combination of N and R. And this is going to evaluate to give us N factorial over n minus R. Factorial times R factorial. So we're going to need to use this formula to evaluate the given combination here, N is going to equal to 13 and R is going to equal to six. So plugging this into the general formula for combinations is going to give us N factorial which is 13 factorial over n minus R which is 13 minus six factorial times R factorial which is six factorial. Now 13 minus six is going to give us seven. So we have 13 factorial over seven factorial times six factorial. Now we can go ahead and simplify this by using the rule for factorial And that states that if you are given a number and factorial this is just a product of the number times all of the terms decreasing by one. So n factorial is equal to n times n minus one times n minus two and so on and so on. So we can go ahead and use this rule to expand our numerator in order to expand 13 factorial we can go ahead and write it out as times 12 times 11 times 10 times nine times eight times seven factorial. And that's all going to be over seven factorial times six factorial. Now notice that we have a seven factorial in both the numerator and denominator, we can go ahead and cancel those out and what we are left with is times 12 times 11 times 10 times nine times 8/6 factorial. And in order to evaluate six factorial, we need to go ahead and expanded six factorial can be expanded as six times five times four times three times two times one. So taking the product of the entire numerator is going to give us 1230, and that's going to be over. The product of the denominator which is going to be 720. And this entire number can be reduced to 1,716 which is going to be the solution or the simplified version of the given expression. And that means that the answer to this problem is going to be d So I hope this video helps you understand how to evaluate a combination and then go ahead and see you all in the next video

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In Exercises 9–16, use the formula for nCr to evaluate each expression. 11C4