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Letters of the word BOSTON are shuffled to form six-letter word. In ho

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Letters of the word BOSTON are shuffled to form six-letter word. In ho  [#permalink]

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New post Updated on: 31 Mar 2018, 01:08
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  55% (hard)

Question Stats:

45% (01:14) correct 55% (02:05) wrong based on 45 sessions

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Letters of the word BOSTON are shuffled to form six-letter word. In how many of all the possible resultant words does B come before N?

A. 120
B. 180
C. 240
D. 360
E. 720

Source :- globalexperts

Originally posted by rishabhmishra on 30 Mar 2018, 22:53.
Last edited by Bunuel on 31 Mar 2018, 01:08, edited 1 time in total.
Edited the question.
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Re: Letters of the word BOSTON are shuffled to form six-letter word. In ho  [#permalink]

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New post 31 Mar 2018, 01:50
The word BOSTON can be arranged in 6!/2! ways.
And B,N can be arranged within themselves in 2! ways. But only one of these will have B before N.
So 6!/(2!+2!) = 180
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Re: Letters of the word BOSTON are shuffled to form six-letter word. In ho  [#permalink]

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New post 31 Mar 2018, 01:51
rishabhmishra wrote:
Letters of the word BOSTON are shuffled to form six-letter word. In how many of all the possible resultant words does B come before N?

A. 120
B. 180
C. 240
D. 360
E. 720

Source :- globalexperts



Total ways to firm six letter word =6!/2!=360..
B before N...
Half of 360 will have B before N and other half N before B..
So ans =360/2=180

B
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Re: Letters of the word BOSTON are shuffled to form six-letter word. In ho  [#permalink]

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New post 31 Mar 2018, 01:54
ankush8998 wrote:
The word BOSTON can be arranged in 6!/2! ways.
And B,N can be arranged within themselves in 2! ways. But only one of these will have B before N.
So 6!/(2!+2!) = 180


Logic is correct but you are wrong in coloured portion..
It will be 6!/(2!*2!) And not 6!/(2!+2!)..
Answer is still correct because 2!+2!=2!*2!
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Letters of the word BOSTON are shuffled to form six-letter word. In ho &nbs [#permalink] 31 Mar 2018, 01:54
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Letters of the word BOSTON are shuffled to form six-letter word. In ho

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