A bag has 4 white, 5 red, and 6 blue balls. Three are drawn at random. What is the probability all three are red?

Given data

• Total balls = 4 + 5 + 6 = 15.
• Red balls = 5.

Concept/ApproachUse combinations without replacement: P(all red) = C(5,3) / C(15,3).

Step-by-step calculationFavourable = C(5,3) = 10Total = C(15,3) = 455Probability = 10/455 = 2/91

Verification/AlternativeSequential draw: (5/15) × (4/14) × (3/13) = 60/2730 = 2/91.

Common pitfallsUsing permutations or treating draws as independent with replacement.

Final Answer2/91