A band has 25 new songs, how many different ways are there for the group to record a CD consisting of 12 songs chosen from 25 new songs. ( The order in which the songs appear on the CD is relevant).
25*24*23*....14 or
25!/(25-12)!
DJ Jacqueline is making a playlist for an mp3 player; she is trying to decide what
12
12
songs to play and in what order they should be played. If she has her choices narrowed down to
21
21
blues,
13
13
reggae, and
25
25
hip-hop songs, and she wants to play an equal number of blues, reggae, and hip-hop songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.
To determine the number of different ways for the group to record a CD consisting of 12 songs chosen from 25 new songs, we can use the concept of combinations. In this case, the order of the songs on the CD is relevant, so we need to use permutations.
The formula for permutations is given by:
P(n, r) = n! / (n - r)!
Where:
n is the total number of items (songs in this case),
r is the number of items to be chosen (songs on the CD in this case),
! denotes the factorial.
Let's calculate this:
P(25, 12) = 25! / (25 - 12)!
= 25! / 13!
Now, we need to calculate the factorial of both 25 and 13.
Factorial of a number is calculated by multiplying all positive integers less than or equal to that number. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.
Using a calculator or programming tool to calculate factorials, we get:
25! = 15511210043330985984000000
13! = 6227020800
Now, substitute these values back into the permutation formula:
P(25, 12) = 15511210043330985984000000 / 6227020800
Calculating this value, we get:
P(25, 12) = 22,078,903,760
Therefore, there are 22,078,903,760 different ways for the group to record a CD consisting of 12 songs chosen from 25 new songs, with the order of the songs on the CD being relevant.