A disc jockey (DJ) has 8 songs to play. Four are slow songs, and 4 are fast songs. Each song is to be played only once. a) In how many ways can the

[Arlivegea]

A disc jockey (DJ) has
8
songs to play.
Four
are slow songs, and
4
are fast songs. Each song is to be played only once.

a) In how many ways can the DJ play the
8
songs if the songs can be played in any order?
b) In how many ways can the DJ play the
8
songs if the first song must be a slow song and the last song must be a slow song?
c) In how many ways can the DJ play the
8
songs if the first two songs must be fast songs?

 

[Muddyakka]

This is not a calculus question, but rather a combinatorics question.

Since you have only given us the question I will assume you do not know where to start.

I find for questions like these you should consider step by step the choices available.

_ _ _ _ _ _ _ _ _

First consider the first song. How many songs can be played first?

Then consider the second. Since you must have played one song first, now how many can you play?
...
Repeat this logic for all 8 slots, and remember that since you are playing ALL 8 songs that it is multiplicative not additive.

If you apply this logic to all 3 parts of the question, they can be solved.

Please reply if you are still confused but otherwise good luck

 

[nasi112]

If Khan would not get angry, I would try to solve this problem!

 

[JeffM]

Do you know the difference between a permutation and a combination?