Combining probability and counting techniques?

DJ Jill is making a playlist for work; she is trying to decide what 12songs to play and in what order they should be played.Step 1 of 2 : If she has h

DJ Jill is making a playlist for work; she is trying to decide what 12

songs to play and in what order they should be played.
Step 1 of 2 :

If she has her choices narrowed down to 3
jazz, 6 blues, 7 disco, and 5 country songs, and she wants to play no more than 3 disco songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

or:DJ Jill is making a playlist for work; she is trying to decide what 12songs to play and in what order they should be played.Step 1 of 2 : If she has her choices narrowed down to 3jazz, 6 blues, 7 disco, and 5 country songs, and she wants to play no more than 3 disco songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

or:The \"naive\" yet correct approach in this case is to fixate & summarise the number of disco tracks, which is a mutually exclusive choice.Ie how many choice have 0 disco + 12 others, (1 + 11), (2 + 10), (3 + 9) then sum; and don't forget to multiply the disco choice by each. 'Others' can be counted as a single group.

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