GMAT Questions Chat Group

In your first case (1112), you chose a tea which would have 3 cups chosen (3C1). Then, you also had to choose a tea that would have 1 cup chosen (2C1). This is correct. This term (3c1 x 3c3 x 2c1 x 3c1 = 18) is correct imo.

Your second case (1122) is where I think the error is. In reality, both the teas chosen have 2 cups chosen each. In other words, you should actually do 3C2 (in how many ways can I choose 2 teas out of 3 for the purposes of taking 2 cups each from the tea). So, actually 3c2 (2 choose the 2 teas) x 3c2 (for cups - 1 of the 2 teas chosen) x 3c2 (for cups - the other tea chosen) = 27. This gives a total of 45. 45/9c4 = 5/14.

In essence, i believe that a double count is happening in your 2nd case (1122) because of the 2C1.

I found it easier to use the complement method here. 1 - (no of ways of ensuring at least 1 tea is tasted).

Edit: I meant 1 - P(all 3 teas are tasted at least once)

Judgement call in my case. But if you think about it, the first question asks us to find max value of "B alone". This does suggest that even if I work with (A+B+C - (II ) - 2(III)), I would eventually need to arrive at B alone. Hence, why not use - a+b+c+d+e+f+g+n(none) = total.