In Exercises 1–8, use the formula for nPr to evaluate each expres...

Question

In Exercises 1–8, use the formula for nPr to evaluate each expression.

9P4

Accepted Answer

hey everyone here we are asked to use the formula for NPR to solve the expression 11 P. Two. So now before we can begin solving we need to recall the formula for N. P. R. Which is N factorial divided by the quantity of n minus R factorial. So now all we have to do is identify the values for N. And R. In really to our given expression here. So starting with N. We see that it's on the left hand side of P. And in our given expression that term is 11. So we can see that N is equal to 11. And then our other term here to the right hand side is the value for our so we see that R. Is equal to two. And now with these values identified we can just plug them into our formula. So we have 11 P two is equal to in the numerator we have n factorial so we'll have factorial. And then in the denominator we have the quantity of N which is 11 minus R. Which is two factorial. And now we can just simplify. So first let's keep the numa later the same as factorial. And then for the denominator we have 11 minus two giving us nine factorial and now we can expand out the numerator here. This factorial until it becomes nine factorial which we have as the denominator. So doing this we have 11 times times nine factorial In the numerator. And then in the denominator we still have this nine factorial and because we did this we now have a nine factorial in the numerator and the denominator, which both cancel. So we are left with just 11 times 10, which multiplying these terms together, we get our final answer here of 110 which is our answer here for choice B. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 1–8, use the formula for nPr to evaluate each expression. 9P4

Key Concepts

Permutations

Factorial

nPr Formula

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