Different words are being formed by arranging the letters of the w | Filo
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Class 11

Math

Algebra

Permutations and Combinations

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Different words are being formed by arranging the letters of the word ARRANGE. All the words obtained are written in the form of a dictionary
Number of ways (words) in which neither two A's nor two R's comes together

  1. None of these
Correct Answer: Option(c)
Solution: Number of ways in which 2 A's are not together =

Among these, let us find the cases when the 2 R's are together.

So, leaving the 2 A's, we have: RR, N, G, E i.e. 4 objects to be arranged in ways.

There are 5 gaps (including the ones at the ends) for placing the 2 A's which can be done in ways. 

Thus, total cases where A's are not together while R's are together =

Thus, cases where A's are not together and R's are not together =

Hence, (c) is correct.
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