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.

7C7

Accepted Answer

Hello. Today we are asked to evaluate the following combination using the general formula for combinations. So what we are given is the combination of 15 and 15. Now the general form of the combination is 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 rule to evaluate the given combination. Here we are given the combination of 15 and 15. We're going to allow end to equal to 15 and are two equal to 15 And plugging this into the general combination is going to give us n factorial which is 15 factorial over N -R which is 15 -15 factorial times r factorial which is 15 factorial. Now here 15 -15 is going to give us zero. So we have 15 factorial over zero factorial times 15 factorial. Now one thing to understand is that zero factorial automatically evaluates to give us one so we can go ahead and replace zero factorial with one. And what we are left with is 15 factorial over one times 15 factorial which is just going to give us 15 factorial. Now what we have is 15 factorial over 15 factorial. Since there's 15 factorial in both the numerator and denominator we can just go ahead and cancel us out to give us 1/1 and that's going to evaluate to just give us one which is going to be the simplified version of the given expression. And that means that the answer to this problem is going to be. Be so. I hope this video helps you in understanding how to evaluate a combination and I'll go ahead and I'll see you all in the next video.