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

Question

Evaluate the expression. *permutation notation* the number of permutations 8 things taken 3 at a time (sub 8)P(sub 3)

Accepted Answer

Welcome back. I'm so glad you're here. We have got the permutation. 10 things taken two at a time written without the numbers there. We know that that's N. Things taken R at a time. So now we can label N equals 10 and R equals two. We know from previous lessons that the formula for permutation is N. Factorial divided by parentheses N minus R. And parentheses factorial. So now we can just fill in the ends and the ours. So in the numerator we've got 10 factorial over and is 10 again minus R. Is two. And parentheses factorial simplified. We've got 10 factorial over 10 minus two is eight factorial. Now I'm going to write out the next step long form so that you can see what we're doing and in the future skip this step. So the numerator R factorial tells us we've got 10 times nine times eight times seven times six times five times four times three times two times one few. The denominator, eight times seven times six times five times four times three times two times one. Great. Now let's see if we've got any factors, these are all being multiplied that cancel out. Starting with the denominator we've got the eight and eight in the numerator and working our way down all of these cancel out from eight all the way down to one. Great. That just leaves us with 10 times nine. Well, another way to think about. This is our numerator was 10 times nine times eight factorial eight all the way down to one divided by that eight factorial we had So we can cancel out our eight factorial as we just saw above, leaving us with both times 10 times nine, which is 90. We look at our answer choices and that matches with answer choice. A while done, we'll catch you on the next one.

Evaluate the expression. permutation notation the number of permutations 8 things taken 3 at a time (sub 8)P(sub 3)

Key Concepts

Permutations

Factorial

Combination vs. Permutation

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