how many 4 letter words can be formed from the word MORADABAD?
MORADABAD has 9 letters out of which 2 are D's, 3 are A's and rest all are distinct.
(i) Choosing all four distinct letters:
There are 6 distinct letter is M, O, R, A, D, B, out of which 4 can be chosen in 6C4 ways. Each letter can be arranged in 4! ways.
∴ Total number of words = 6C4 × 4!
(ii) Two distinct and two alike:
Pairs of alike letters are DD, AAA, out of which one pair can be chosen in 2C1 ways.
Two distinct letters out of remaining 5 types of letters can be chosen in 5C2 ways.
Total number of ways = 2C1 × 5C2
(iii) Two alike of one kind and two alike of second kind:
There are two sets of alike letters, out of these two are to be selected in 2C2 ways.
(iv) Three alike and one distinct:
There is one set of three alike letters, and it can be selected in one way.
Out of 5 different letters, one can be selected in 5C1 ways.
Hence, the total number of 4-letter words = 360 + 240 + 6 + 20