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805+ Level|   Combinations|      
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Bunuel
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In how many ways the letters of the word "LOCKDOWN" can be arranged 12 Jan 2022, 02:30
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

25% (02:09) correct 75% (01:54) wrong based on 126 sessions

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In how many ways the letters of the word "LOCKDOWN" can be arranged such that N is always between O's?

A. 720
B. 1440
C. 2520
D. 4320
E. 6720


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E
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In how many ways the letters of the word "LOCKDOWN" can be arranged 12 Jan 2022, 05:32
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Bunuel
In how many ways the letters of the word "LOCKDOWN" can be arranged such that N is always between O's?

A. 720
B. 1440
C. 2520
D. 4320
E. 6720


Are You Up For the Challenge: 700 Level Questions

 
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Number of ways LOCKDOWN can be rearranged = 8!/2! |O is coming twice.
Now in 1/3rd of the cases N will come between O's.
So, 8!/2!*3 will give us = 6720.
E as the answer­
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In how many ways the letters of the word "LOCKDOWN" can be arranged 13 Jan 2022, 02:08
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"such that N is always between O's" - does this mean 'ONO' only or does it also include 'OLKNO' for example?

If the former i.e. 'ONO' only, would it not be similar to considering 'T' = 'ONO' and the options become how you can arrange 'T'LCKDW which is 6! = 720?
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In how many ways the letters of the word "LOCKDOWN" can be arranged 13 Jan 2022, 04:45
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Aham56
"such that N is always between O's" - does this mean 'ONO' only or does it also include 'OLKNO' for example?

If the former i.e. 'ONO' only, would it not be similar to considering 'T' = 'ONO' and the options become how you can arrange 'T'LCKDW which is 6! = 720?
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It means N is between two O's not between two O's only.

LOCKDOWN
cases: OCKDWNOL, ONOCKDWNL and so on. Every third number will be like that. Hence division by 3.
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In how many ways the letters of the word "LOCKDOWN" can be arranged 16 Jan 2022, 16:54
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I still don't understand why every three permutations will have an 'N' between two 'O's
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sk070
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In how many ways the letters of the word "LOCKDOWN" can be arranged 20 Jan 2022, 07:09
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ElninoEffect
Aham56
"such that N is always between O's" - does this mean 'ONO' only or does it also include 'OLKNO' for example?

If the former i.e. 'ONO' only, would it not be similar to considering 'T' = 'ONO' and the options become how you can arrange 'T'LCKDW which is 6! = 720?


It means N is between two O's not between two O's only.

LOCKDOWN
cases: OCKDWNOL, ONOCKDWNL and so on. Every third number will be like that. Hence division by 3.
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Could you please elaborate on how to find every 3rd case would have N between?

TIA!

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jasminelin
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In how many ways the letters of the word "LOCKDOWN" can be arranged 20 Mar 2022, 20:45
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Aham56
"such that N is always between O's" - does this mean 'ONO' only or does it also include 'OLKNO' for example?

If the former i.e. 'ONO' only, would it not be similar to considering 'T' = 'ONO' and the options become how you can arrange 'T'LCKDW which is 6! = 720?


It means N is between two O's not between two O's only.

LOCKDOWN
cases: OCKDWNOL, ONOCKDWNL and so on. Every third number will be like that. Hence division by 3.

Could you please elaborate on how to find every 3rd case would have N between?

TIA!

Posted from my mobile device
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because you can have ONO, OON, or NOO with spaces between each or not
only ONO will have N in between, so 1/3 of the options
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In how many ways the letters of the word "LOCKDOWN" can be arranged 07 Jun 2022, 07:22
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Bunuel
In how many ways the letters of the word "LOCKDOWN" can be arranged such that N is always between O's?

A. 720
B. 1440
C. 2520
D. 4320
E. 6720


Are You Up For the Challenge: 700 Level Questions
 

Number of ways LOCKDOWN can be rearranged = 8!/2! |O is coming twice.
Now in 1/3rd of the cases N will come between O's.
So, 8!/2!*3 will give us = 6720.
E as the answer
Show more
Can you elaborate a bit more on Now in 1/3rd of the cases N will come between O's. this specific part?­
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In how many ways the letters of the word "LOCKDOWN" can be arranged 07 Jun 2022, 20:45
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Bunuel
In how many ways the letters of the word "LOCKDOWN" can be arranged such that N is always between O's?

A. 720
B. 1440
C. 2520
D. 4320
E. 6720


Are You Up For the Challenge: 700 Level Questions
 
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I think this question is tougher than any that I've seen in under the "Elementary Combinatorics" heading of the OGs since about the year 2000. I doubt you'd get a question like this on the test anymore. Alas, I'm a nerd and it's fun, so here goes.

If we ignore the ONO limitation, we have 8!/2!.

How many of those arrangements will have the N before both of the Os? Well, if we ignore the other letters and just look at the N and two Os, the N will be first 1/3rd of the time.
Similarly, the N will be between the Os 1/3rd of the time.
And the N will be after the Os 1/3rd of the time.

We are only allowed to include arrangements where the N is between the Os, so we need 1/3rd of 8!/2!.

8*7*6*5*4 = 56*120 = 56*100 + 56*20 = 5600 + 1120 = 6720

Answer choice E.­
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In how many ways the letters of the word "LOCKDOWN" can be arranged 19 Feb 2025, 03:10
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