In Exercises 1–8, evaluate the given binomial coefficient.

Question

Accepted Answer

Hey everyone here we are asked to find the value of the binomial coefficient for the expression 17/1. Now here before we start solving we need to recall the formula to calculate a binomial coefficient which says that the expression N K is equal to N factorial divided by K factorial times the quantity of n minus K factorial. So now we just need to look at our given expression and determine our N and K values. So our top value is 17, so our end is going to be equal to 17 and then our lower value is one. So we know that K is going to be equal to one. And now we can just take these values and plug them into our formula and we see that our expression 17 1 is equal to In the numerator we have n factorial. So we have 17 factorial divided by K factorial which is one factorial times the quantity of N which is again -1 which is K. And with this we can just start simplifying. So for now keeping the numerator the same. We have 17 factorial divided by one factorial And then we have 17 -1 giving us 16 factorial. And now with this 16 factorial we can expand our numerator to have a 16 factorial as well. So we have in the numerator 17 times factorial, all divided by the one factorial times factorial. And now we can clearly see that the 16 factorial R in the numerator and the denominator. So they cancel out. And we're left with 6 17 Divided by one factorial, which is just one. Therefore our final simplified coefficient is just 17. Leaving us with answer choice. D. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

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In Exercises 1–8, evaluate the given binomial coefficient.