Question

SAT Question - Help?

The Hungry Ghosts are a rock band that can play 7 different songs. FOr an upcoming show, the Hungry Ghosts have time to play only 4 songs in their set. If a set consists of 4 songs in a specific order, how many different sets do the Hungry Ghosts have the option of playing at their upcoming show.

Answer : 840

How do I do this?

Answer 1

Have you studied permutations?

Answer 2

Sort of?
I know it's something order dependent.

Answer 3

The n umber of permutations of n different things taken r at a time is:
\[\large P(n, r)=\frac{n!}{(n-r)!}=\frac{7\times6\times5\times4\times3\times2\times1}{3\times2\times1}=you\ can\ calculate\]

Answer 4

@kropot72
How about the formula for combinations? Does it look similar to that?
And thanks for the formula much easier than how my teacher explained it.

Answer 5

I get the top part of n! but can you explain what r is?

Answer 6

The formula that I posted for permutations is 'without repetitions'.
With repetitions the number of permutations is:
\[\large n ^{r}\]
The number of combinations of n different things taken r at a time is:
\[\large C(n, r)=\frac{n!}{r!(n-r)!}\]
r is the number of the n different things taken at a time. In the question that you posted, r is the number of songs in a set which is 4.

Answer 7

Oh okay so it was 7-4 so find the r.
So is that how you usually find r?
Haha sorry if this is a dumb question.

Answer 8

In the question, n = 7 being the total number of different songs. r = 4 being the number of songs taken at a time:
\[\large n-r=7-4=3\]

Answer 9

Thank you very much