Final answer:
There are 56 total ways to choose two red marbles without replacement from a bag of 10 blue and 8 red marbles. This is calculated by multiplying the number of ways to choose the first red marble (8) by the number of ways to choose the second red marble (7).
Step-by-step explanation:
How many ways can two red marbles be chosen successively from a bag containing 10 blue marbles and 8 red marbles, without replacement? To solve this, we follow the principle of combinatorics using the formula for combinations since the order in which we choose the marbles does not matter. The formula for combinations is C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and '!' denotes factorial.
- First, we need to find the number of ways to choose the first red marble. There are 8 red marbles to choose from, so there are 8 ways.
- Since we are not replacing the first red marble, there are now 7 red marbles left for the second choice.
- The number of ways to choose the second red marble is, therefore, 7.
To find the total number of ways to choose two red marbles without replacement, we multiply the number of ways to choose the first red marble by the number of ways to choose the second red marble:
8 (first choice) × 7 (second choice) = 56 total ways to choose two red marbles without replacement.
The answer is 56, which corresponds with option C.