A bag contains five red marbles and three blue marbles. In how many different ways can two red marbles be drawn if the first marble is not returned to the bag before the second marble is drawn?
To find the number of different ways to draw two red marbles, we need to use the concept of combinations.
First, let's number the red marbles as R1, R2, R3, R4, and R5. To draw two red marbles without replacement, we need to select two marbles from the five available. The order in which we select the marbles does not matter.
The formula for finding the number of combinations is given by nCr = n! / (r! * (n-r)!), where n represents the total number of objects and r represents the number of objects to choose.
In this case, n = 5 (number of red marbles) and r = 2 (number of marbles to choose).
So, the number of ways to draw two red marbles from the bag is:
nCr = 5! / (2! * (5-2)!)
= 5! / (2! * 3!)
= (5 * 4 * 3!) / (2! * 3!)
= (5 * 4) / (2 * 1)
= 10
Therefore, there are 10 different ways to draw two red marbles from the bag without replacement.