George has a bag of marbles. Inside the bag are 5 red marbles, 3 green marbles, and 2 blue marbles. He draws out two marbles in a row, without replacement. What is the number of outcomes?

To find the number of outcomes, we need to first determine the total number of marbles and then calculate the number of ways two marbles can be drawn without replacement.

In this case, George has a total of 5 red marbles + 3 green marbles + 2 blue marbles = 10 marbles in the bag.

To find the number of ways two marbles can be drawn, we need to use the concept of combinations. The formula for combinations is:

nCr = n! / (r!(n-r)!)

Where n is the total number of items and r is the number of items taken at a time.

In this case, n = 10 (total number of marbles) and r = 2 (number of marbles drawn).

Substituting the values into the formula:

10C2 = 10! / (2!(10-2)!)
= 10! / (2!8!)
= (10 x 9 x 8!) / (2! x 8!)
= (10 x 9) / 2!
= 90 / 2
= 45

Therefore, the number of outcomes is 45.