GMAT Club Around The World!!! How many different words, with or withou

Question

How many different words, with or without meaning, can be formed by shuffling the alphabets of MIRANDA such that M always comes before R in the words formed?

A. 420
B. 630
C. 840
D. 1260
E. 1680

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Bunuel · Accepted Answer

Experts' Global Video Official Explanation

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ElninoEffect · Answer

Number of ways word MIRANDA can be rearranged = 7!/2!
Number of ways in which M comes before R = 1/2 of the total cases, In other half cases R will come before M.

So total number of ways = 7!/2!*2! = 1260   D

Kinshook · Answer

Asked: How many different words, with or without meaning, can be formed by shuffling the alphabets of MIRANDA such that M always comes before R in the words formed?

M-1
I - 1
R-1
A-2
N-1
D-1
Total - 7

Total number of words that can be formed by shuffling alphabets of MIRANDA = 7!/2! = 2520
Number of words such that M always comes before R in the words formed = 2520/2 = 1260

IMO D

gmatophobia · Answer

Total number of possible arrangements =  \frac{ 7 ! }{ 2 !}  = 2520

In 50% of the arrangements M always comes before R. Hence,  \frac{ 2520 }{ 2 }  = 1260

IMO D

100mitra · Answer

1st Number of ways alphabet can be arrangement : MIRANDA = 7 alphabet = 7!
but repeated words "A" is twice 2!
its (7! / 2!) = 2520 ways

2nd M must be before R always = 6!+5!+4!+3!+2!+1! = 873 (Addition "or" either of the possiablities of event)
M can be arranged in 6! before R@7th Position 
M can be arranged in 5! before R@6th Position
M can be arranged in 4! before R@5th Position
M can be arranged in 3! before R@4th Position 
M can be arranged in 2! before R@3th Position 
M can be arranged in 1! before R@2th Position

thus 2520 - 873 = "1647"

sajibdas · Answer

Solution: 5!/2!*6 + 5!/2!*5 + 5!/2!*4 + 5!/2!*3 + 5!/2!*2 + 5!/2!*1 = 360 + 300 + 240 + 180 + 120 + 60 = 1260 
So, the ans will be option D.

ParitoshRawat99 · Answer

The total number of words which can be possibly made = 7!/2! = 2520
Total number of words in which R comes before M = Total number of words in which M comes before R 
And,
The interesting thing about this is that these would constitute to the total number of words.

Thus the number of words in which M comes before R is = 2520/2 = 1260

Thus, IMO answer = D (1260)

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