Total ways to draw 4 marbles from 15:
Related Articles
- Question: A circular throughfall in a coral reef has a diameter equal to the diagonal of a 6 cm by 8 cm rectangular coral fragment. What is the circumference of the throughfall?
- Solution: The diagonal of the rectangle is $ \sqrt{6^2 + 8^2} = 10 $ cm. The circumference is $ \pi \times \text{diameter} = 10\pi $ cm. The circumference of the throughfall is $\boxed{10\pi}$ cm.**Question:** A bag contains 7 red marbles and 8 blue marbles. If four marbles are drawn at random, what is the probability that exactly two are red?
- To solve this problem, we use combinations to determine the number of ways to draw marbles with the specified conditions.
- The total number of ways to draw 4 marbles from a bag containing 7 red and 8 blue marbles is given by:
- \binom{15}{4} = \frac{15 \times 14 \times 13 \times 12}{4 \times 3 \times 2 \times 1} = 1365
- Ways to draw exactly 2 red marbles:
