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

Question

Exercise 7: Evaluate the binomial coefficient (100 choose 2).

Accepted Answer

Hey everyone here we are asked to calculate the value of the binomial coefficient for the following expression 98 and three. Now before we saw this we need to recall the formula for calculating a binomial coefficient and it states that the egg expression N K is equal to n factorial divided by K. Factorial times the quantity of n minus K factorial. So now we just want to identify our values for n N K in relation to our given expression. So the top value here in our expression is 98, so N is going to be equal to 98 and the lower value is three, so K is equal to three. And now with these values let's just Plug them into our formula and we can find our coefficient. So beginning in the numerator we have n factorial but instead of N we have 98. So we have 98 factorial divided by K factorial or three K times the quantity of N which is 98 minus K, which is three factorial. Now we just need to start simplifying. So keeping the numerator the same for now we have 98 factorial divided by three factorial times minus three which gives us 95 factorial. And now since we have this 95 factorial in the denominator we can expand the numerator. This 98 factorial until we also have a 95 in the numerator. So doing this we have 98 times 97 times, 96 times 95 factorial in the numerator. And And in the denominator we still have three factorial times factorial. And now we can clearly see that the 95 factorial is canceled out. So we are left with again in the numerator times 97 times 96. And in the denominator we have three factorial, which expands to three times two times one. And now multiplying these terms together and simplifying. We see that our binomial coefficient comes out to 152,096, which is our answer here for choice d thanks for watching. I hope you found this video helpful and I'll see you again next time.

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

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