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?

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.

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JeanaShupp JeanaShupp · Answer 2 · 2019-09-17T16:22:34+02:00

Answer: 125970

Step-by-step explanation:

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

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

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

[tex]^{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[/tex]

Hence, the number of different playlists are possible= 125970