Last visit was: 03 Jun 2024, 21:28 It is currently 03 Jun 2024, 21:28
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6817
Own Kudos [?]: 30421 [5]
Given Kudos: 799
Location: Canada
Send PM
All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink] All 6 letters from the set {L, O, B, O, M, O} are randomly selected on   06 May 2022, 07:52
3
Kudos
2
Bookmarks
Expert Reply
Top Contributor
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

77% (01:35) correct 23% (01:29) wrong based on 52 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
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?

(A) 1/120
(B) 1/240
(C) 1/360
(D) 1/720
(E) 1/1440
ShowHide Answer
Official Answer
A
User avatar
L
PyjamaScientist
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Posts: 1130
Own Kudos [?]: 1072 [2]
Given Kudos: 629
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Send PM
Reviews Badge
All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink] All 6 letters from the set {L, O, B, O, M, O} are randomly selected on   06 May 2022, 08:29
1
Kudos
1
Bookmarks
There are 6 alphabets in total. "O" repeats three times.

So, the total number of arrangements that we can make using these 6 alphabets (incorporating three O's) = \(\frac{6!}{3!} = 120.\)

Now, the arrangement BLOOOM will be one of the 120 total possible arrangments using the given alphabets. Thus, the probability of getting that one arrangement is \(\frac{1}{120}\). (A)
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 7901
Own Kudos [?]: 4142 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User
Re: All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink] All 6 letters from the set {L, O, B, O, M, O} are randomly selected on   06 May 2022, 09:06
Ways to arrange LOBOMO :6!/2!;120
witthouy replacement BLOOM can be arranged in 1 way so P 1/120
Had it been without replacement then 2/120: 1/60


BrentGMATPrepNow 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?

(A) 1/120
(B) 1/240
(C) 1/360
(D) 1/720
(E) 1/1440


Posted from my mobile device
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6817
Own Kudos [?]: 30421 [2]
Given Kudos: 799
Location: Canada
Send PM
Re: All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink] All 6 letters from the set {L, O, B, O, M, O} are randomly selected on   06 May 2022, 09:34
1
Kudos
1
Bookmarks
Expert Reply
Top Contributor
BrentGMATPrepNow 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?

(A) 1/120
(B) 1/240
(C) 1/360
(D) 1/720
(E) 1/1440


The two solutions above are perfect.
Those solutions involved counting methods, so here's a solution that uses probability rules.

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: A
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 33299
Own Kudos [?]: 833 [0]
Given Kudos: 0
Send PM
Re: All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink] All 6 letters from the set {L, O, B, O, M, O} are randomly selected on   07 May 2024, 02:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: All 6 letters from the set {L, O, B, O, M, O} are randomly selected on [#permalink]
07 May 2024, 02:24
Moderator:
Bunuel
Math Expert
93473 posts