Jeffrey, a DJ at a local radio station, is choosing the music he will play on his shift. He must choose all his music from the top 100 songs for the week and he must play at least 12 songs an hour. In his first hour, all his choices must be from the top-20 list.

a) In how many ways can Jeffry choose the songs for his first hour if he wants to choose exactly 12 songs?

b) In how many ways can Jeffry hoose the 12 songs if he wants to pick 8 of the top 10 and 4 from the songs listed from 11 to 20 on the chart?

c) In how many ways can he choose either 12 or 13 songs to play in the first hour of is shift?

d) In how ways can he choose the songs if he wants to play upto 15 songs in the first hour

Step-by-step explanation:

a) In how many ways can Jeffrey choose the songs for his first hour if he wants to choose exactly 12 songs?  

the answer i got was 20C12 = 125970

b) In how many ways can Jeffrey choose the 12 songs if he wants to pick 8 of the top 10 and 4 from the songs listed from 11 to 20 on the chart?

He has to choose 8 from 10 and 4 from 10. C(10,8)C(10,4)

c)In how many ways can Jeffrey choose either 12 or 13 songs to play in the first hour of his shift?

When it is OR, you can add them instead of multiplying. See why? They are independent.  C(20,13)+C(20,12)

d)In how many ways can Jeffrey choose the songs if he wants to play up to 15 songs in the first hour?  

Remember, he must play at least 12. So, he plays at least 12 but up to 15.

(-5,-28)

i graphed to on desmos.