We have got 6 types of letters. We have to form words of 4 letters. We consider four cases

(i) All 4 different : Selection

Arrangement

(ii) Two different and two alike :

and in ways. Having chosen one pair we have to choose 2 different letters out of the remaining 5 different letters in ways. Hence the number of selections is . Each of the above 30 selections has 4 letters out of which 2 are alike and they can be arranged in ways.

Hence number of arrangements is .

(iii) 2 like of one kind and 2 of other :

Out of these sets of three like letters we can choose 2 sets in ways. Each such selection will consist of 4 letters out of which 2 are alike of one kind, 2 of the other. They can be arranged in ways.

Hence the number of arrangements is .

(iv) 3 alike and 1 different :

There is only one set consisting of 3 like letters and it can be chosen in 1 way. The remaining one letter can be chosen out of the remaining 5 types of letters in 5 ways.

Hence the number of selection . Each consists of 4 letters out of which 3 are alike and each of them can be arranged in ways.

Hence the number of arrangements is .

From (i), (ii), (iii) and (iv), we get

Number of selections

Number of arrangements

.