The letters of the word MIRANDA are shuffled. What is the probability

Question

The letters of the word MIRANDA are shuffled. What is the probability that the new word formed is MANDIRA?

A. 1/7!
B. 2!/7!
C. (2!2!)/7! 
D. 12/7!
E. 2/6!

Shreya1211 · Answer

Bunuel   GMATNinja  explanation please?

(I selected A)

Arungmat612 · Answer

Total possibilities are 7!/2!.
And there can be only one possibility of getting MANDIRA.
Therefore 1/7!/2!, which gives 2!/7!.

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GMATNinja · Answer

Remember that the pool of letters includes not one but TWO letter A's, which we can think of as A(1) and A(2).

The 7! options include two distinct options that spell MANDIRA:

MA(1)NDIRA(2)
 
 MA(2)NDIRA(1)

So the numerator needs to be 2 (2!=2) and not 1.

einstein801 · Answer

Hi  GMATNinja  is it not 2*2/7! given that MANDIRA has two ways of being formed due to the 2 As?

Bunuel · Answer

No need to overcomplicate this—it’s an easy question. There are seven letters in MIRANDA, with A repeating twice. The total number of  different  words that can be formed by arranging these letters is 7!/2!. Only one of those arrangements will be MANDIRA, so the probability is 1/(7!/2!) = 2!/7!.

Answer: B.

The letters of the word MIRANDA are shuffled. What is the probability

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The letters of the word MIRANDA are shuffled. What is the probability