How many different ways can you arrange three songs on a CD? (Show the steps you did please.)

Asked on by gw1974

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Matthew Fonda | eNotes Employee

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We know we must place three songs on a CD. Let's call our three songs A, B, and C.

We first must choose the song #1. Since we haven't chosen any songs yet, we have three choices, A, B, or C. Say for example we choose A. Next, we must pick the second song, and since we have already used A, we now have only two choices, B or C. Say we pick B. This leaves only one choice for the third song, C.

Since we had three choices for the first song, two for the second, and one for the third, the total number of ways to arrange three songs on a CD is 3*2*1 = 6. We could also write this as 3! (3 factorial).

(Using this same logic, you could see that for example if you had asked for 5 songs, there are 5*4*3*2*1 = 120 ways to do it. We call this a permutation).

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