There are twenty songs from which a disc jockey can chose five to play on her program. How many different arrangements of songs are possible for the program?
Please check my work
20x19x18x17x16
That is correct.
To calculate the number of different arrangements of songs, where the order matters, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, the order of the songs matters because each song will be played in a specific position on the program.
To find the total number of arrangements, we multiply the number of choices for each position. In this scenario, there are 20 songs available for the first position, 19 songs available for the second position, 18 songs available for the third position, 17 songs available for the fourth position, and 16 songs available for the fifth position.
So the calculation would be:
20 * 19 * 18 * 17 * 16 = 1,860,480
Therefore, there are 1,860,480 different arrangements of songs possible for the program.