Question

A disc jockey has 20 songs to choose from and can only play 8 in the next half hour. how many different playlists are possible?

Answer 1

Answer: 125970

Step-by-step explanation:

The number of combinations of n things taken r at a time is given by :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

Similarly , the  number of combinations of 20 songs taken 8 at a time is given by :-

$^{20}C_8=\dfrac{20!}{8!(20-8)!}\\\\=\dfrac{20\times19\times18\times17\times16\times15\times14\times13\times12!}{8\times7\times6\times5\times4\times3\times2\timews12!}\\\\=125970$

Hence, the number of different playlists are possible= 125970

Answer 2

This problem is a combination problem since it did not indicate that there is a specified order of songs to be played. The type of combination problem is without repetition. Thus the working equation would be n!/r!(n-r)! wherein n is the total number of songs to choose from and r is the number of songs you can choose at a given time. The answer would be 125970.