This is a question from "GMAT Official Guide 2019 Quantitative Review" and it says, "A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?" The answer is 315
1. I did 7 times 10 times 9 equals 630. 630/3 equals 210. For the first job, any 7 will do. For the second any 10 will do and for the third any 9 will do, so multiply them all and you 630. Since they want sets of three, you do 630/3 = 210.
2. 7 plus (10 times 9) == 97. You don't mulitply 7, 10, and 9 because the math department is different from the computer science department. You can just add them and I didn't bother to divide by 3 because the correct answer is 315 not 97.
I don't understand what they mean when they wrote, "If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?"
1. I did 7 times 10 times 9 equals 630. 630/3 equals 210. For the first job, any 7 will do. For the second any 10 will do and for the third any 9 will do, so multiply them all and you 630. Since they want sets of three, you do 630/3 = 210.
2. 7 plus (10 times 9) == 97. You don't mulitply 7, 10, and 9 because the math department is different from the computer science department. You can just add them and I didn't bother to divide by 3 because the correct answer is 315 not 97.
I don't understand what they mean when they wrote, "If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?"