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All 6 letters from the set {L, O, B, O, M, O} are randomly selected on

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Carcass
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All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink] New post   05 May 2022, 06:19
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All 6 letters from the set {L, O, B, O, M, O} are randomly selected one at a time without replacement. What is the probability the 6 letters (in the order they were selected) spell BLOOOM?

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1/120



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Re: All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink] New post   05 May 2022, 11:46
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This is a very good question, will wait for OE
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Re: All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink] New post   07 May 2022, 05:15
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Carcass wrote:
All 6 letters from the set {L, O, B, O, M, O} are randomly selected one at a time without replacement. What is the probability the 6 letters (in the order they were selected) spell BLOOOM?

Show: ::
1/120



P(letters spell BLOOOM) = P(1st letter is B AND 2nd letter is L AND 3rd letter is O AND 4th letter is O AND 5th letter is O AND 6th letter is M)
= P(1st letter is B) x P(2nd letter is L) x P(3rd letter is O) x P(4th letter is O) x P(5th letter is O) x P(6th letter is M)
= 1/6 x 1/5 x 3/4 x 2/3 x 1/2 x 1
= 1/120

Answer: 1/120
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Re: All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink] New post   07 May 2022, 11:40
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Thanks for explanation GreenlightTestPrep
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All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink] New post   25 Mar 2023, 06:46
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We can also approach it as a combinations/selection (P & C) question. The total number of ways in which letters LOBOMO can be selected is 6!/3! since number of letters is 6 and frequency of O is 3.
And the number of ways we can get BLOOOM = 1
Therefore, Probability of getting BLOOOM out of {L, O, B, O, M, O} = 1/(6!/3!) = 3!/6! = 1/4x5x6 = 1/120
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Re: All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink] New post   14 Aug 2025, 18:12
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink]
14 Aug 2025, 18:12
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