Question

The number of four letter words that can be formed by taking the letters of the word KANYAKUMARI is

• A. 2218
• B. 1680
• C. 1708
• D. 1714

Answer 1

The correct option is A 2218

In the word there are 2 K's and 3 A's and 6 different letters N,Y,U,M,R,I
Number of words with all 4 letters different $=$ ${}^8{C}_4$ $=$ 1680
Number of words with 3 letters alike (K letter) and 1 different $=$ ${}^7{C}_1\frac{4!}{3!}$ $=$ 28
Number of words with 2 letters alike (K or A) of one type and another 2 alike (K or A) of other type $=$ $\frac{4!}{2!\times 2!}$ $=$ 6
Number of words with 2 letters alike (K or A) and 2 letters different $=$ ${}^2{C}_1{.}^7{C}_2\frac{4!}{2!}$ $=$ 504
Total is $2218$