Two sets of marbles, ABC and DEF. What's the probability of choosing a combination of ABC, my favorites?

Question

Assume you choose one marble at a time until you have 3 selected. Remember, order is not important. You can draw C first or A or B.

Answer 1

Let's look at the prob of choosing A, B and C in that order first.
This is 1/6 * 1/5 * 1/4 = 1/120
If order is not important, then there are 3! = 6 of arranging A, B and C.
So prob = 6 / 120 = 1/20

Answer 2

The first marble can be abc and not def, so 3/6. Let's say you choose A.

The second marble can be bc and not def, so 2/5. Let's say you choose B.

The third marble can only be c and not def, so 1/4.

3/6 * 2/5 * 1/4 = 6/120 = 1/20

Answer 3

(3/6)*(2/5)*1/4=1/20

Answer 4

50% chance