How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first three letters must be THM

120 ways

Step-by-step explanation: The word ALGORITHM has 9 letters. We want them to be written in a row, which means, order of the letters are important, so, use Permutation.

Permutation is calculated by:

P(n,r) =

We want to use 6 of the 9 letters with first 3 being THM. So, n = 6 and r = 3:

Permutation will be:

P(6,3) =

P(6,3) =

P(6,3) = 120

There are 120 ways six letters of ALGORITHM be written in a row with first three letters THM.