Evaluate the expression. *permutation notation* the number of per...

Question

Evaluate the expression. *permutation notation* the number of permutations 9 things taken 5 at a time (sub 9)P(sub 5)

Accepted Answer

Welcome back. I'm so glad you're here. We've got a permutation. We've got 14 things taken three at a time written without the numbers in there. That would be end things taken R at a time so we can label N equals 14 and R equals three. And we recall from previous lessons that the formula for permutation is N. Factorial. In the numerator over parentheses and minus R. And parentheses factorial. Now we can just fill in for N. And R. So in the numerator we've got 14 factorial divided by N 14 minus R minus three and parentheses factorial. We can simplify. So we've got 14 factorial divided by 11 factorial. Alright I'm going to write this out longhand so that you can see what we're doing and in the future if you understand this you can skip this step. So in the numerator we've got 14 times 13 times 12 times times 10 times nine times eight times seven times six times five times four times three times two times one, breathe. And in the denominator slightly shoulder we've got 11 times 10 times nine times eight times seven times six times five times four times three times two times one. That's what factorial are Looking at the factors we've got written here, starting with the 11 in the denominator we've got an 11 in both the denominator and the numerator and continuing on down with these numbers all the way to one. They cancel out leaving us just with 14 times 13 times 12. Well we could think about this step in a more abbreviated way. We could say that in the numerator we've got 14 times times 12 times 11 factorial And in the denominator we've got 11 factorial. And we know we just saw that those 11 factorial cancel out Both situations leave us with 14 times 13 times 12. And our calculator tells us that that is 2,184. Giving us answer choice. C. Well done, we'll catch you on the next one.

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Evaluate the expression. permutation notation the number of permutations 9 things taken 5 at a time (sub 9)P(sub 5)