George has a bag of marbles. Inside the bag are 5 red marbles, 3 red marbles, and 2 blue marbles. He draws out two marbles in a row, without replacement. What is the number of outcomes?
clearly a typo ...
I will read the second bag to have 3 white marbles
RWB
RBB
RWW
WWW
BBB
RRR
To determine the number of outcomes, you need to consider the number of ways George can choose two marbles from the bag without replacement.
First, calculate the total number of marbles in the bag:
5 red marbles + 3 red marbles + 2 blue marbles = 10 marbles
To calculate the number of outcomes when drawing two marbles without replacement, you will use a combination. The formula for calculating combinations is:
nCr = n! / (r!(n-r)!)
Where:
n = total number of marbles to choose from
r = number of marbles to be chosen
In this case, n = 10 (total marbles) and r = 2 (number of marbles George is drawing in a row).
Now, substituting n = 10 and r = 2 into the formula:
10C2 = 10! / (2!(10-2)!)
= 10! / (2! * 8!)
= (10 * 9 * 8!) / (2! * 8!)
= (10 * 9) / (2 * 1)
= 45
Therefore, the number of outcomes when George draws two marbles in a row from the bag without replacement is 45.