Evaluate the given expression. 9 P 4 _9P_4 9 P 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 am 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.

4. Probability

Counting

Statistics

4. Probability

Counting

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Multiple Choice

Evaluate the given expression. $_9P_4$

$24$

$3,024$

$15,120$

$362,880$

Verified step by step guidance

Understand the notation: The expression 9P4 represents a permutation, which is the number of ways to arrange 4 items out of 9 distinct items.

Recall the formula for permutations: The formula for permutations is given by $ nP_r = \frac{n!}{(n-r)!} $, where $ n $ is the total number of items, and $ r $ is the number of items to arrange.

Apply the formula: For 9P4, substitute $ n = 9 $ and $ r = 4 $ into the formula. This gives $ 9P4 = \frac{9!}{(9-4)!} $.

Calculate the factorials: Compute $ 9! $ and $ 5! $. Remember that $ n! $ (n factorial) is the product of all positive integers up to $ n $.

Divide the factorials: Divide $ 9! $ by $ 5! $ to find the number of permutations, which will give you the final result.

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Evaluate the given expression. $_9P_4$