A bag contains 7 red, 5 orange, and 6 green jellybeans. What is the probability of reaching into the bag and randomly withdrawing 12 jellybeans such that the number of red ones is 6, the number of orange ones is 4, and the number of green ones is 2? Express your answer as a fraction or a decimal number rounded to four decimal places.

Probability of reaching into the bag and randomly withdrawing 12 jellybeans such that the number of red ones is 6, the number of orange ones is 4, and the number of green ones is 2 is (525/18564) = 0.0283

Step-by-step explanation:

We need to select 6 red jelly beans from 7 red ones, 4 Orange jelly beans from 5 Orange ones and 2 green jelly beans from 6 green ones.

This can be done in the following way

⁷C₆ × ⁵C₄ × ⁶C₂ = 7 × 5 × 15 = 525

But totally, 12 jelly beans can be selected from 18 jelly beans in

¹⁸C₁₂ = 18564

Probability of reaching into the bag and randomly withdrawing 12 jellybeans such that the number of red ones is 6, the number of orange ones is 4, and the number of green ones is 2 is

525/18564 = 0.0283