Total ways to draw 4 marbles from 15:

February 22, 2026

Total ways to draw 4 marbles from 15:

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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:

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