Question

5a. DJ Mykel is making a playlist for a website; he is trying to decide what 15 songs to play and in what order they should be played.

If he has his choices narrowed down to 6 blues, 4 reggae, 6 country, and 7 jazz songs, and he wants to play no more than 2 reggae songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

5b. The newly elected president needs to decide the remaining 8 spots available in the cabinet he/she is appointing. If there are 14 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?

Answer 1

Answer:

5b)

Given ,

There are 8 spots available for 14 positions

To determine the number of different ways can the members of the cabinet be appointed

Here we apply permutations for this

i.e., 8 out of 14

= 14P8

= 14! / (14-8)!

= 14! / 6!

= 121080960

Hence the number of different ways can the members of the cabinet be appointed is 121080960