Question

DJ Larissa is making a playlist for an mp3 player; she is trying to decide what 9 9 songs to play and in what order they should be played. Step 1 of 2 : If she has her choices narrowed down to 7 7 hip-hop, 7 7 disco, 6 6 jazz, and 5 5 rock songs, and she wants to play no more than 4 4 rock songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Answer 1

Solution:-

Total no of songs=7+7+6+5=25

If rock = 0,So no of ways=20C₉=167960

If rock =1, So no of ways=5C₁*20C₈=629850

If rock =2, So no of ways=5C2*20C7=775200

If rock =3, So no of ways=5C3*20C6​​​​​​​=387600

If rock =4, So no of ways=5C4*20C₅=77520

Total=2038130

ordered is also mentioned

Hence,

Required answer is=2038130*9!

=739596614400

=7.39 x 10^{​​​​​​​11}