Question

DJ Erin is making a playlist for work; he is trying to decide what 10 songs to play and in what order they should be played. Step 1 of 2 : If he has his choices narrowed down to 3 country, 6 pop, 7 disco, and 3 hip-hop songs, and he wants to play no more than 3 pop songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Answer 1

Answer:

211*10⁹

Step-by-step explanation:

Total songs = 3country + 6pop + 7 disco + 3hip-hop  = 19 songs

Max pop songs = 3

Case 1: no pop songs;

¹³C₁₀*⁶C₀= 286

Case 2: 1 pop song ;

¹³C₉*⁶C₁= 4290

Case 3: 2 pop songs;

¹³C₈*⁶C₂= 19305

Case 4: 3 pop songs;

¹³C₇*⁶C₃= 34320

Total = 58201

so, now if order is also to be considered for making playlists then the number of playlists is =58201*10! = 211*10⁹