Question

in how many ways can the letters of the word PROBLEM be rearranged to make seven letter word the arrangement need to be meaningful such that none of the letters repeat

Answer 1

There are seven positions to be filled.

The first position can be filled using any of the 7 letters contained in PROBLEM.

The second position can be filled by the remaining 6 letters as the letters should not repeat.

The third position can be filled by the remaining 5 letters only and so on.

Therefore, the total number of ways of rearranging the 7 letter word =

7*6*5*4*3*2*1 = 7! ways.