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Question

The number of permutations of the word BIOLOGY is


  1. 1680

  2. 2520

  3. 720

  4. 840


Solution

The correct option is B

2520


In the word BIOLOGY, there are 7 letters, in which O appears 2 times  and B,I,L,G,Y each appears once.

Therefore, the required number of arrangements 7!2!=2520

Explanation:-
O appears 2 times.
Temporarily, let us treat these repeated letters different and name them as O1,O2 .
The number of permutations of 7 different letters, in this case, taken all at a time is 7!.
One such permutation is O1BLIGYO2.
Here if O1,O2 are not same, then they can be arranged in 2! ways.
Therefore 2! permutations will be just the same permutation corresponding to this chosen permutation O1BLIGYO2.
Hence the total number of different permutations will be 7!2!=2520

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