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Three new students are to be assigned at random to 5 empty dormitory r

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Carcass
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Three new students are to be assigned at random to 5 empty dormitory r [#permalink] New post   21 Jan 2022, 07:00
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Three new students are to be assigned at random to 5 empty dormitory rooms. What is the probability that all the three students will be assigned to the same room?

(A) \(\frac{1}{5}\)

(B) \(\frac{1}{10}\)

(C) \(\frac{1}{15}\)

(D) \(\frac{1}{25}\)

(E) \(\frac{1}{30}\)
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Re: Three new students are to be assigned at random to 5 empty dormitory r [#permalink] New post   21 Jan 2022, 10:00
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Carcass wrote:
Three new students are to be assigned at random to 5 empty dormitory rooms. What is the probability that all the three students will be assigned to the same room?

(A) \(\frac{1}{5}\)

(B) \(\frac{1}{10}\)

(C) \(\frac{1}{15}\)

(D) \(\frac{1}{25}\)

(E) \(\frac{1}{30}\)

P(all 3 students assigned to same room) = P(1st student is assigned to ANY room AND 2nd student assigned to same room as 1st student AND 3rd student assigned to same room as 1st student)
= P(1st student is assigned to ANY room) x P(2nd student assigned to same room as 1st student) x P(3rd student assigned to same room as 1st student)
= 5/5 x 1/5 x 1/5
= 1/25

Answer: D
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gmatclubot
Re: Three new students are to be assigned at random to 5 empty dormitory r [#permalink]
21 Jan 2022, 10:00
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