The word BOOKKEEPING has eleven letters, of which two are O’s, two are K’s, two are E’s and five different letters are B, P, I, N and G.

The word with five letters : ___, ____, ____, ____, ____, ____.

First place filled with letter O = 2!.

Second place filled with letter K = 2!.

Third place filled with letter E = 2!.

Fourth and fifth places are filled with five different letter B, P, I, N and G = P(5, 2) = 5!/(5 - 2)! =  5!/3!.

From the Fundamental Counting Principle : m · n

= 2! · 2! · 2! · (5!/3!)

= 2 · 2 · 2 · [ (1 · 2 · 3 · 4 · 5) / (1 · 2 · 3) ]

= 8 · [ 4 · 5 ]

= 160.