Question 16

# How many 4 letter words can be formed from the word "CORONAVIRUS".

Solution

"CORONAVIRUS" has 7 distinct alphabets and two pairs of repeated characters ", O" and "R".

There are three possible cases for creating 4 letter words.

1. Two letters are "O" and the other two are "R".

The total number of arrangements = $$\frac{4!}{2!\times2!}=6$$

2. Two of the letters are either "O" or "R" and the others are distinct.

The total number of arrangements = $$^2C_1\times^8C_2\times\frac{4!}{2!}=2\times28\times12=672$$

3. All four letters are distinct.

The total number of arrangements = $$^9C_4\times4!=3024$$

Thus, the total number of four-letter words possible = $$6+672+3024=3702$$.

Hence, the answer is option C.

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##### Ishan Patni

4 months ago

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##### Ali

8 months, 4 weeks ago

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