Problem

Steve wants to download a selection of new music. How many ways can Steve select two rock songs, two alternative songs, and nine rap songs from a list of four rock songs, seven alternative songs, and ten rap songs?
There are ways that Steve can select his songs.

Answer

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Answer

Final Answer: There are \(\boxed{1260}\) ways that Steve can select his songs.

Steps

Step 1 :Steve wants to download a selection of new music. How many ways can Steve select two rock songs, two alternative songs, and nine rap songs from a list of four rock songs, seven alternative songs, and ten rap songs?

Step 2 :This is a combination problem. We need to find the number of ways to select two rock songs from four, two alternative songs from seven, and nine rap songs from ten. The formula for combination is \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and ! denotes factorial.

Step 3 :The number of ways to select two rock songs from four is \(C(4, 2) = 6\).

Step 4 :The number of ways to select two alternative songs from seven is \(C(7, 2) = 21\).

Step 5 :The number of ways to select nine rap songs from ten is \(C(10, 9) = 10\).

Step 6 :The total number of ways that Steve can select his songs is the product of the number of ways to select the rock, alternative, and rap songs. So, \(6 \times 21 \times 10 = 1260\).

Step 7 :Final Answer: There are \(\boxed{1260}\) ways that Steve can select his songs.

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