Number of words of 4 letters that can be formed with the letters of the word IIT JEE, is

Options

A. 42
B. 82
C. 102
D. 142

Answer

C

Explanation

There are 6y letters I,I,E,E,T,J
The following cases arise:
Case I All letters are different
`.^(4)C_(4)=4!=24`
Case II Two alike and two different
`.^(2)C_(1)xx.^(3)C_(2)xx(4!)/(2!)=72`
Case III Two alike of one kind and two alike of another kind
`.^(2)C_(2)xx(4!)/(2!2!)=6`
Hence, number of words=24+72+6=102