Question

A bag contains 5 red marbles, 3 green, 1 lavender, 3 yellow, 2 Orange.

Q. How many sets of four marbles include none of the red ones?

First I computed C(14,4) to find out how many sets of 4 could be formed. Total # sets =1001.

Then I subtracted the number of sets with 1, 2, 3, and 4 red marbles:

C(5,1) x C(9,3) = 84
C(5,2) x C(9,2) = 360
C(5,3) x C(9,1) = 180
C(5,4) = 5
Total sets with red marbles = 629

Final answer = 1001 - 629 = 372

Is this correct?