4. Probability

Counting

4. Probability

Counting

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Multiple Choice

Emily is organizing her closet. She has 15 shirts left to hang but has space in one section for 6 shirts. How many ways could she hang shirts in that section?

$3,603,600$

$90$

$9$

$362,880$

Verified step by step guidance

Identify the problem as a permutation problem where Emily needs to select and arrange 6 shirts out of 15.

Use the permutation formula, which is given by: P(n, r) = n! / (n - r)! where n is the total number of items to choose from, and r is the number of items to arrange.

Substitute the values into the formula: n = 15 and r = 6, so the formula becomes: P(15, 6) = 15! / (15 - 6)!.

Calculate the factorials: 15! and 9! (since 15 - 6 = 9). Factorials are calculated by multiplying all positive integers up to that number.

Divide 15! by 9! to find the number of ways Emily can arrange 6 shirts out of 15.

7:11m

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