Question

A recording artis plans to place six songs on her new CD. i) In how many ways can she order these songs? ii) In how many ways can She order these songs if she has already chosen the first and last selections?

Answer 1

Okay, let's solve these step-by-step:

i) There are 6 songs that can be arranged in any order. To calculate the number of possible arrangements (orders), we use the factorial formula:

Number of arrangements = 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720

So there are 720 ways to order the 6 songs.

ii) Now the first and last songs are fixed, so we only have 4 songs left to arrange. Again using the factorial formula:

Number of arrangements = 4! = 4 * 3 * 2 * 1 = 24

So with the first and last songs fixed, there are 24 ways to order the remaining 4 songs.

In summary:

i) 6! = 720 ways

ii) 4! = 24 ways

Let me know if you have any other questions!