Question

A composer’s guild is planning its spring concert, and ten pieces have been submitted for consideration. The director of the guild knows that they will only have time to present four of them. If the pieces can be played in any order, how many combinations of pieces are possible?

Answer 1

The number of combinations of four pieces out of ten for the concert is 5040.

Step-by-step explanation:

The number of combinations of four pieces out of ten can be found using the concept of permutations. We can use the formula for permutations of n objects taken r at a time, which is given by nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects to be chosen. In this case, n = 10 and r = 4.

So, the number of combinations of four pieces out of ten is 10P4 = 10! / (10-4)! = 10! / 6! = 10 * 9 * 8 * 7 = 5040.

Therefore, there are 5040 possible combinations of pieces that can be played in the concert.