Question

The number of permutations of the word BIOLOGY is

• A. 2520
• B. 2000
• C. 800
• D. 2500

Answer 1

The correct option is A 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 $\frac{7!}{2!}=2520$

Explanation:-
O appears 2 times.
Temporarily, let us treat these repeated letters different and name them as $O_1,O_2$ .
The number of permutations of 7 different letters, in this case, taken all at a time is 7!.
One such permutation is $O_{1}BLIGY{O}_2$.
Here if $O_1$,$O_2$ 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 $O_{1}BLIGY{O}_2$.
Hence the total number of different permutations will be $\frac{7!}{2!}=2520$