DJ Joyce is making a playlist for a website; she is trying to decide what 6
songs to play and in what order they should be played. If she has her choices narrowed down to 16 pop, 7reggae, and 22 blues songs, and she wants to play an equal number of pop, reggae, and blues songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.
I need statistics help, I'm stuck on this question?
- Posted:
- 3+ months ago by whoknows101
- Topics:
- homework, question, statistics, statistic
Details:
Answers (2)
So you want 2 out 0f 15, 2 out of 7, and 2 out of 22.
There are 16 choices for the first song, 15 for the second, 7 for third, 6 for fourth, 22 for fifth, and 21 for sixth.
16 x 15 x 7 x 6 x 22 x 21 = 4.65696000 x 10^6
It makes no sense to round to 1/100 place, since you can't have a fraction of a song. But there it is anyway.
The general rule for the number of possibilities p of ordering k items out of a set of n items is:
p = n! / (n - k)!
In our case, keeping Joyce's self imposed constraints in mind:
there are 3 subsets:
P = 16 pop songs
R = 7 reggea songs
B = 22 blues songs
k = 2, as Joyce wants to pick 2 songs out of each subset to finally present a playlist of 6 songs on the website. (Lists are ordered, sets are not.)
For k = 2 the formula p = n! / (n - k)! reduces to n * (n - 1). Let's plug in values:
p_P = 16 * 15 * 14! / 14! = 15 * 16 = 240
Now we do this again for R & B (pun intended ;)
p_R = 7 * 6 = 42
p_B = 22 * 21 = 462
And finally we put it all together:
p_playlist = 240 * 42 * 462 = 4 656 960
Rounded to two decimal places:
4.66 * 10^6 possibilities to order the playlist