Answer:
She can make up her 10 song playlist in 3195116 ways
Step-by-step explanation:
7 blues, 6 disco, 8 pop, 4 hip hops
Total songs = 25
She wants to play no more than 4 disco songs in a playlist of 10 songs
Meaning the music can be grouped as disco and other music genres.
Disco songs = 6
Other genres = 19
She can make up her 10 song playlist in any of the following ways.
- 10 other genres, 0 disco song
This playlist can be made in
¹⁹C₁₀ ways = 92378 ways
- 9 other genres, 1 disco song
This playlist can be made in
¹⁹C₉ × ⁶C₁ = 92378 × 6 = 554268 ways
- 8 other genres, 2 disco song
This playlist can be made in
¹⁹C₈ × ⁶C₂ = 75582 × 15 = 1133730 ways
- 7 other genres, 3 disco song
This playlist can be made in
¹⁹C₇ × ⁶C₃ = 50388 × 20 = 1007760
- 6 other genres, 4 disco song
This playlist can be made in
¹⁹C₆ × ⁶C₄ = 27132 × 15 = 406980
Total number of ways = 92378 + 554268 + 1133730 + 1007760 + 406980 = 3195116 ways
