NDA 2 2025 Maths, question 105

Topic: Probability

Q105

An urn contains $5$ white, $6$ red and $4$ blue balls. Three balls are drawn at random. What is the probability that a white ball, a red ball and a blue ball are drawn?

(a) $28/91$
(b) $2/7$
(c) $24/91$ Correct answer
(d) $23/91$

Solution.

Answer: (c) $24/91$

Choose one ball of each colour in 5×6×4=120 ways.
There are C(15,3)=455 equally likely unordered triples, giving 120/455=24/91.
This agrees with summing the six possible colour orders for sequential draws.