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?

What is 3*3? Nine possible outcomes

RG
RR
RB
BG
GG
RR
BB
GR
BR

To find the number of outcomes, we need to consider the possible combinations of marbles that George can draw out of the bag. Since he is drawing two marbles in a row without replacement, the order in which he draws the marbles does not matter. In other words, drawing a red marble first and then a green marble is considered the same as drawing a green marble first and then a red marble.

To calculate the number of outcomes, we can use the concept of combinations. The formula for calculating the number of combinations is:

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

Where n is the total number of objects and r is the number of objects chosen. In this case, we have 10 marbles in total (5 red, 3 green, and 2 blue), and we want to choose 2 marbles.

Using the formula, the number of outcomes can be calculated as:

10C2 = 10! / (2!(10-2)!)
= 10! / (2!8!)
= (10 * 9 * 8!) / (2! * 8!)
= (10 * 9) / 2!
= (10 * 9) / (2 * 1)
= (90) / 2
= 45

Therefore, the number of outcomes is 45.