Permutations and Combinations
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
- 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.