Multiple choice

A box contains $10$ red marbles, $20$ blue marbles and $30$ green marbles, $5$ marbles are drawn at random from the box, what is the probability that a ll are blue?

  1. $\dfrac {34}{11977}$
  2. $\dfrac {34}{11966}$
  3. $\dfrac {68}{11977}$
  4. $\dfrac {68}{11966}$
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A Correct answer
Explanation

Total marbles = 10 + 20 + 30 = 60. Probability of drawing 5 blue marbles = (20C5) / (60C5). 20C5 = (20*19*18*17*16) / (5*4*3*2*1) = 15504. 60C5 = (60*59*58*57*56) / (5*4*3*2*1) = 5461512. Ratio = 15504 / 5461512 = 34 / 11977.

AI explanation

The total number of marbles is 60, so the number of ways to draw 5 marbles from the box is 60C5, which equals 5461512. The number of ways to draw 5 blue marbles from the 20 available is 20C5, which equals 15504. The probability is 15504 divided by 5461512, which simplifies to 34 divided by 11977. The result is 34/11977.

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