Question

trying to decide what 10 songs to play and in what order they should be played If he has his choices narrowed down to 6 hip-hop, 4 pop, 3 reggae, and 8 blues songs, and he wants to play no more than 2 pop songs, how many different playlists are possible

Answer 1

262548

Explanation:

Given that :

Hip-hop =6

Pop = 4

Reggae = 3

Blues = 8

Total number of songs :

Total Pop songs = 4

Others = 6 + 3 + 8 = 17

To have no more Than 2 pop songs :

Pop songs = 0 ; others = 10

17C10 * 4C0 = 19448 * 1 = 19448

Pop songs = 1 ; others = 9

17C9 * 4C1 = 24310 * 4 = 97240

Pop songs = 2 ; others = 8

17C8 * 4C2 = 24310 * 6 = 145860

Total number of ways :

(19448 + 97240 + 145860) = 262548