Question

The organizer of a conference is selecting workshops to include. She will select from 10 workshops about genetics and 7 workshops about ethics. In how many

ways can she select 9 workshops if more than 6 must be about genetics?

Answer 1

To solve this problem, we can use combinations.

First, let's find the total number of ways to select 9 workshops from the 17 available:

Total number of ways = (17 choose 9) = 24310

Next, let's find the number of ways to select 6 or fewer workshops about genetics:

Number of ways to select 0 genetics workshops = (7 choose 9) = 0
Number of ways to select 1 genetics workshop = (7 choose 8) x (10 choose 1) = 70
Number of ways to select 2 genetics workshops = (7 choose 7) x (10 choose 2) = 45
Number of ways to select 3 genetics workshops = (7 choose 6) x (10 choose 3) = 300
Number of ways to select 4 genetics workshops = (7 choose 5) x (10 choose 4) = 2100
Number of ways to select 5 genetics workshops = (7 choose 4) x (10 choose 5) = 2520
Number of ways to select 6 genetics workshops = (7 choose 3) x (10 choose 6) = 4200

Now we can subtract the number of ways to select 6 or fewer workshops about genetics from the total number of ways to select 9 workshops:

Number of ways to select more than 6 genetics workshops = 24310 - 70 - 45 - 300 - 2100 - 2520 - 4200 = 12075

Therefore, there are 12,075 ways to select 9 workshops if more than 6 must be about genetics.