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 nine p four or the number of permutations of four objects out of a total of nine 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 nine p four. So I know that my value for n is this nine and then my value for r is four. Now plugging this into my permutations formula, I know that I have nine factorial on the top and then on the bottom doing n minus r factorial, I get nine minus four factorial. Now simplifying that denominator, in my numerator I still have that nine factorial and then in the denominator nine minus four will give me five, and then that's five 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 nine times eight times seven times six times five factorial because that's what I'm trying to cancel in my denominator. So since I have that five factorial on the bottom, that's now going to cancel, and I'm simply left with a nine times eight times seven times six. Now fully multiplying that out gives me 3,024, which is my final answer here that the number of permutations of four objects out of nine total objects is 3,024. Thanks for watching and let me know if you have questions.

4. Probability

Counting

Statistics for Business

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

The formula for permutations is given by: P(n, r) = n! / (n-r)!, where 'n' is the total number of items, and 'r' is the number of items to arrange.

Substitute the values into the formula: P(9, 4) = 9! / (9-4)!.

Calculate the factorials: 9! (9 factorial) is the product of all positive integers up to 9, and 5! (5 factorial) is the product of all positive integers up to 5.

Divide the factorial of 9 by the factorial of 5 to find the number of permutations: P(9, 4) = 9! / 5!.

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Evaluate the given expression. $_9P_4$