How many different arrangements can be made by taking 5 of the letters of the word EQUATION ?

There are 8 different letters in the word equation.

 

To make a 5 letter word using the letters of the word EQUATION, the first position from (the left most position) can be filled up by using any of the 8 letters.

So, this position can be filled up by 8 ways.

 

The next position (right of left most position) can be filled up by 7 ways. The next three positions can be filled up by 6, 5 and 4 ways.

 

Therefore, the number of different arrangements those can be made by taking 5 of the letters of the word EQUATION = 8 × 7 × 6 × 5 × 4 = 6720.