Find the number of four letter words which can be made using the letters of the word "HIPPOPOTAMUS", if not all four letters are different.

Answer

`0710`

Explanation

No. of words when it contains
(a) 3 alike , 1 different ` to 1 xx ""^(8) C_1 xx (4!)/(3!) = 32 `
(b) 2 alike , 2 alike ` to 1 xx (4!)/(2! 2!) = 6`
(c ) 2 alike , 2 different , 1 different ` to 2 xx ""^(8)C_2 xx (4!)/(2!) = 672`
Total number of required words = 710