Evaluate the given binomial coefficient
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Hello. Today we're going to be evaluating a binomial coefficient. So before we jump into this let's just quickly recall what the binomial coefficient is equal to. So if you have a binomial coefficient in the form of n K, this is going to equal to n factorial over n minus K factorial times K factorial. So in order to evaluate this, let's go ahead and figure out what our N and K is. So once again N is the top number of the binomial coefficient and K is the bottom number of the binomial coefficient. So n is equal to nine and K is equal to four. And all we're gonna do is go ahead and plug those numbers into this expansion. So what we have is n factorial or nine factorial over n minus K or nine minus four factorial times K factorial which is four factorial. Okay, so 9 -4 is going to give me five. So what we have is nine factorial over five factorial times four factorial. And we can go ahead and expand the numerator to be nine times eight times seven times six times five factorial and all of that is gonna be over five factorial times four factorial. Now, if you notice we have a product of five factorial in both the numerator and denominator. So we can go ahead and cancel out those quantities and four factorial could be expanded as four times three times two times one. So what we are left with is nine times eight times seven times six. All over four times three times two times one, Multiplying the numerator together is going to give me 3,024 and multiplying the denominator together is going to give me 24 and 3020 for over is going to equal to 126 which is going to be our solution. 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 expand a binomial coefficient and I'll go ahead and see you all in the next video.

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