25*24*23*....14 or
25!/(25-12)!
25!/(25-12)!
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.
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.