Question 1170072: Steve wants to download a selection of new music. How many ways can Steve select four rock songs, three alternative songs, and eleven rap songs from a list of five rock songs, eight alternative songs, and twelve rap songs?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this problem using combinations.
**1. Selecting Rock Songs:**
* Steve needs to select 4 rock songs from a list of 5 rock songs.
* This is a combination problem, as the order in which he selects the songs doesn't matter.
* The number of ways to choose 4 rock songs from 5 is given by the combination formula:
* ⁵C₄ = 5! / (4! * (5-4)!) = 5! / (4! * 1!) = (5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * 1) = 5
**2. Selecting Alternative Songs:**
* Steve needs to select 3 alternative songs from a list of 8 alternative songs.
* The number of ways to choose 3 alternative songs from 8 is:
* ⁸C₃ = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56
**3. Selecting Rap Songs:**
* Steve needs to select 11 rap songs from a list of 12 rap songs.
* The number of ways to choose 11 rap songs from 12 is:
* ¹²C₁₁ = 12! / (11! * (12-11)!) = 12! / (11! * 1!) = 12
**4. Total Number of Ways:**
* To find the total number of ways Steve can select the songs, we multiply the number of ways for each genre:
* Total ways = ⁵C₄ * ⁸C₃ * ¹²C₁₁
* Total ways = 5 * 56 * 12
* Total ways = 3360
**Therefore, there are 3360 ways Steve can select the songs.**
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