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P, Q, R, S, T are camels participating in a race. What is the probability that R will be ranked higher than Q, who in turn will be ranked higher than P? (Assume all the camels are equally competent).

P, Q, R, S, T are camels participating in a race. What is the probability that R will be ranked higher than Q, who in turn will be ranked higher than P? (Assume all the camels are equally competent). Correct Answer 1/6

Five horses can be arranged in 5 positions in 5! Ways = 120 different ways

Three horses P, Q, R can be arranged in 3! Ways = 6 different ways

Out of these 6, there is only one way in which R is ranked higher than Q, who in turn is ranked higher than P

⇒ Out of 120 arrangements of 5 horses, there are (1/6) × 120 = 20 different arrangements in which R is ranked higher than Q, who in turn is ranked higher than P

⇒ Required probability = 20/120

⇒ 1/6

∴ Required Probability = 1/6

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