Question

How many words can be created with the words COMBINATION, with two identical and two different characters?

Answer 1

In word COMBINATION

There are three sets of two same letters i.e I I , O O , N N

and

There are 6 distinct letters.

Out of 3 sets of two same letters one set can be chosen in ways 3C1

and

From the remaining 6 distinct letters, 2 letters can be chosen in ways 6C2

Thus 2 same letters and 2 different letters can be selected in ways =

(3C1*6C2)

So there are (3C1*6C2) group of 4 letters each.

Hence, the total number of words consisting two same letters and 2 different = (3C1*6C2) * 4!/2! = 540

540 is required answer.