DJ Bronson is making a playlist for a demo CD; he is trying to decide what 10 songs to play and in what order they should be played. Step 2 of 2 : If he has his choices narrowed down to 7 blues, 6 rock, 4 country, and 6 jazz songs, and he wants to play all 7 blues songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Since DJ Bronson wants to make a playlist of 10 songs and has his choices narrowed down to 7 blues, 6 rock, 4 country, and 6 jazz songs, and he wants to play all 7 blues songs.

Since the order matters in the arrangement of the songs and 7 blues songs are playing, we use permutation, So, we have 7! ways of arranging the 7 blues songs.

We are left with space for three other songs.

Since we have 6 rock, 4 country, and 6 jazz songs, the number of ways of arranging 6 rock songs is ⁶P₁ = 6. The number of ways of arranging 4 country songs is ⁴P₁ = 4, and the number of ways of arranging 6 jazz songs is ⁶P₁ = 6.

So, the total number of ways of arranging all 10 songs is 7! × 6 × 4 × 6 = 725760 ways

= 7.25760 × 10⁵

= 7.26 × 10⁵ different playlists

So, there are 7.26 × 10⁵ different playlists

Learn more about permutations here:

https://brainly.com/question/12974932