how many four letter word can be form using letter of word "INEFFECTIVE"

(i) 3 same 1 different

(ii) 2same of one kind , 2 same of other kind

(iii)2 same, 2distinct

(iv) All different

Dear Student!

Here is the answer to your query.

There are 11 letters in the word INEFFECTIVE i.e E E E, F F, I I, C, T, N, V

(i) There is only one set of three same letters i.e E E E. So three same letters can be selected in one way. Out of 6 different letters F, I, T, N, V, C one letter can be selected in ways. Thus three same and one different letter can be selected in 1 × ways. So there are  group each of which contains 3 same letters. These 4 letter can be arranged in ways.

Hence the total number of words consisting of 3 same and one different letters = =

(ii) There are three sets of  two some letters i.e E E, F F, I I . Out of these three sets two can be selected in ways. So there are group each of which contains 4 letters out of which 2 are same of one type and two are same of second type.Now, 4 letters in each group can be arranged in ways.

Hence the total number of words consisting two same letters of one kind and 2 same letters of other kind

(iii) Out of 3 sets of two same letters one set can be chosen in ways.Now, from the remaining 6 distinct letters, 2 letters can be chosen in ways. Thus 2 same letters and 2 different letters can be selected in ways. So there are group of 4 letters each.

Now, letters of each group can be arranged among themselves in ways.

Hence, the total number of words consisting two same letters and 2 different =

(iv) There are 7 distinct letters E, F, I, T, N, V, C out of which 4 can be selected in   ways. So there are groups of 4 letters each. The letter in each of can be arranged in 4! ways. So the total number of 4 letters words in which all letters are different =

Cheers!