Evaluate the given expression. 9 P 4 _9P_4

Here we're asked to evaluate the given expression, and the expression we're given is 9p4 or the number of permutations of 4 objects out of a total of 9 objects. Now since we're already given this permutations notation here, all that's left to do is to plug this into our permutations formula. So let's go ahead and do that. So I have a 9p4. So I know that my value for n is this 9, and then my value for r is 4. Now plugging this into my permutations formula, I know that I have 9 factorial on the top and then on the bottom doing n minus r factorial, I get 9 minus 4 factorial. Now simplifying that denominator, in my numerator I still have that 9 factorial and then in the denominator 9 minus 4 will give me 5 and then that's 5 factorial. Now from here, we want to go ahead and rewrite our numerator in order to cancel out our denominator. So let's go ahead and do that. So rewriting my numerator, I get 9 times 8 times 7 times 6 times 5 factorial because that's what I'm trying to cancel in my denominator. So since I have that 5 factorial on the bottom, that's now going to cancel and I'm simply left with 9 times 8 times 7 times 6. Now fully multiplying that out gives me 3,024, which is my final answer here, that the number of permutations of 4 objects out of 9 total objects is 3,024. Thanks for watching, and let me know if you have questions.