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The letters "CFOSU" are arranged in dictionary order. What is the rank

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The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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New post 11 Nov 2019, 00:49
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

61% (01:52) correct 39% (01:28) wrong based on 77 sessions

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Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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New post 25 Jan 2020, 08:43
1
1

Solution



Given
In this question, we are given that
    • All the letters of “CFOSU” are arranged in dictionary order

To find
We need to determine
    • The rank of the word “FOCUS”

Approach and Working out
If all the letters are arranged in alphabetical order, then we will have words starting with C first, then F, then O, then S, and finally U.

If C is the first word, then the remaining words can arrange themselves in 4! = 24 ways

Next, we will have words starting with F.
    • Words starting with FC = 3! = 6
    • Words starting with FOC: FOCSU and FOCUS

Hence, the rank of the word FOCUS = 24 + 6 + 1 + 1 = 32

Thus, option D is the correct answer.

Correct Answer: Option D
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Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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New post 11 Nov 2019, 01:30
Bunuel wrote:
The letters "CFOSU" are arranged in dictionary order. What is the rank of the word "FOCUS" in this order?

(A) 17
(B) 21
(C) 31
(D) 32
(E) 38


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CFOSU = 4! ways
FCOSU = 3! ways
FOCSU = 1 and FOCUS ; 1
total 4!+3!+1+1 ; 32
IMO D
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Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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New post 11 Jan 2020, 10:45
Bunuel wrote:
The letters "CFOSU" are arranged in dictionary order. What is the rank of the word "FOCUS" in this order?

(A) 17
(B) 21
(C) 31
(D) 32
(E) 38


Are You Up For the Challenge: 700 Level Questions


Can somebody explain how to approach these questions

Thanks
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Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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New post 25 Jan 2020, 01:12
It would be highly appreciated if someone could elaborate a little bit on this. Thanks
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Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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New post 01 Feb 2020, 07:02
Can anyone recommend more faster or alternative approach here please?
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Re: The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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New post 01 Feb 2020, 07:21
Bunuel wrote:
The letters "CFOSU" are arranged in dictionary order. What is the rank of the word "FOCUS" in this order?

(A) 17
(B) 21
(C) 31
(D) 32
(E) 38


Are You Up For the Challenge: 700 Level Questions


Words starting with letter C = 4! = 24
With F as first letter, words starting with C as second letter = 3! = 6
Words with F as first and C as second letter, O as third letter, S as fourth and U as fifth letter = 1
Ranking of word FOCUS = 24 + 6 + 1 + 1 = 32

IMO D
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The letters "CFOSU" are arranged in dictionary order. What is the rank  [#permalink]

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New post 01 Mar 2020, 01:02
Bunuel wrote:
The letters "CFOSU" are arranged in dictionary order. What is the rank of the word "FOCUS" in this order?

(A) 17
(B) 21
(C) 31
(D) 32
(E) 38




The first word in this order will be CFSOU

With C as starting letters, we have 4! ways = 24 arrangement.
With F as starting letters, we have FSxxx before FOxxx, so 3! = 6 more numbers before FOCUS.
With FO as starting letters, clearly C is the next one to go. So we have FOCxx.

Since U is behind S in the alphabet, we have FOCSU and then FOCUS. The rank of FOCUS is 24+6+1+1 = 32.
IMO D.

I hate this type of question so much. Singing the alphabet song to solve this kind of problems takes a huge toll on my manhood.
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The letters "CFOSU" are arranged in dictionary order. What is the rank   [#permalink] 01 Mar 2020, 01:02
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