JEE Main · 2024 · 06 Apr 2024 · Shift 2 · Probability

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If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is

(A) $\frac{18}{25}$
(B) $\frac{4}{25}$
(C) $\frac{12}{25}$ ✓ Correct
(D) $\frac{6}{25}$

Answer: (C)

Solution

Total ways to post 3 letters to 5 addresses:

5^{3} = 125

. To use exactly 2 addresses: choose the 2 addresses (

(2 5) = 10

ways), then distribute 3 letters onto these 2 addresses using both (

2^{3} - 2 = 6

ways). Favourable outcomes

= 10 \times 6 = 60

, so probability

= \frac{60}{125} = \frac{12}{25}

JEE Main · 2024 · 06 Apr 2024 · Shift 2 · Single correct option

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