In how many ways can the selection be made so that at least one of each color is drawn?

Question

Your urn contains 7 red balls, and 9 blue balls, and you draw 4 balls.

Answer 1

7R, 9B, 4 balls drawn

ways it can get at least 1R and at least 1B are the ways to get exactly 1 of either (8 ways) and exactly 2 of each

RBBB

BRBB

BBRB

BBBR 4 ways to get exactly one Red, another 4 ways to get exactly one Blue

RRBB

RBRR

RBRB

BRRB

BRBR

BBRR 6 ways get exactly 2 of each R and B

total 6+8 = 14 ways to get at least one of each

alternatively calculate the number of ways to get 0 of R or B

two ways: RRRR or BBBB

total ways the balls could be drawn is 2^4 = 16. 16-2 = 14 ways to get at least one R or B

14 is the answer