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We are required to form different words with the help of letters of th

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New post 01 Nov 2019, 05:47
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We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2?

A. 18
B. 24
C. 30
D. 36
E. 40


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Re: We are required to form different words with the help of letters of th  [#permalink]

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New post 01 Nov 2019, 06:21
Bunuel wrote:
We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2?

A. 18
B. 24
C. 30
D. 36
E. 40


Are You Up For the Challenge: 700 Level Questions


Formula: Not together = Total ways - no of ways when together

Number of ways when I&N together = arranging the letters {IN, T, E, G, E, R} in a straight line = 6!*2!/2! = 6! = 720

Total ways of arranging INTEGER = 7!/2! = 2520

Not together, m1 = 2520 - 720 = 1800

Number of ways which begin with I and end with R is same as arranging the letters {N, T, E, G, E} in the given spaces I, _, _, _, _, _, R = 5!/2! = 60 = m2

m1/m2 = 1800/60 = 30

IMO Option C

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Re: We are required to form different words with the help of letters of th  [#permalink]

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New post 01 Nov 2019, 07:55
Bunuel wrote:
We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2?

A. 18
B. 24
C. 30
D. 36
E. 40


Are You Up For the Challenge: 700 Level Questions


INTEGER can be arranged in 7!/2! ways = 2520
M1 = m1 be the number of words in which I and N are never together = INTEGER ; XTEGER = 6!/2!*2c1 ; 720
so M1 = 2520-720 ; 1800
M2 = m2 be the number of words which begin with I and end with R ; I NTEGE R ; 5!/2! ; 60 ways
ratio M1/M2 = 1800/60 ; 30
IMO C
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Re: We are required to form different words with the help of letters of th   [#permalink] 01 Nov 2019, 07:55
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