Evaluate 40!/(4! 38!)

Question

Accepted Answer

Hello. Today we're going to simplify an expression that involves factorial. So the expression given to us is 52 factorial over three factorial times factorial. Now recall that whenever you have a number raised to the factorial for example four factorial what you're really doing is going ahead and taking a product of four times all of its decreasing terms. So four factorial is going to be the same thing as four times three times two times one. And you can also rewrite this with respect to factorial. So if you wanted to you can also rewrite four factorial as four times three factorial. So we're gonna go ahead and use this trick to help us simplify this expression. So if you notice we have a 50 factorial in the denominator and a 52 factorial in the numerator, 52 factorial could be rewritten as 52 times 51 times 50 factorial and all that is going to be over three factorial times 50 factorial. Now the reason why I rewrote this is because this allows us to get a product of 50 factorial in both the numerator and denominator and that allows us to cancel out the 50 factorial without actually having to calculate that product. So what we are left with is 52 times 51/ factorial And three factorial could be rewritten as three times 2 times one. So what that we are left with is 52 times 51/3 times two times one. Now 52 times 51 is gonna give me 2,652 and three times two times one is going to give me six and this is going to simplify to 442 which is going to be our solution. So the answer to this problem is going to be be so I hope this video helps you in understanding how to use Factorial and I'll go ahead and see you all in the next video.

Evaluate 40!/(4! 38!)

Key Concepts

Factorial

Binomial Coefficient

Simplification of Fractions

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