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.

5C0

Accepted Answer

Hello. Today we are asked to use the formula for the combination of N N R. To solve the following expression. So the expression given to us is the combination of 11 and zero. But 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 rule to evaluate the given expression. Well we have the combination of 11 and zero here and is going to equal to 11 and our is going to equal to zero. So plugging this into the general combination is going to give us N factorial which is 11 factorial over n minus R which is 11 minus zero factorial times R factorial which is zero factorial. Now one thing to understand zero factorial automatically evaluates to one. So we can go ahead and replace the zero factorial with one and 11 0 is just going to give us 11. So what we have is 11 factorial over 11 factorial times one which is just 11 factorial. Now we have 11 factorial in both the numerator and denominator. So we can just go ahead and evaluate those to be 1/1. And what we are left with is just one and this is going to be the expression evaluated 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 see all in the next video.

In Exercises 9–16, use the formula for nCr to evaluate each expression. 5C0

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