Answer: 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) = [tex]\frac{n!}{(n-r)!}[/tex]
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) = [tex]\frac{6!}{(6-3)!}[/tex]
P(6,3) = [tex]\frac{6.5.4.3!}{3!}[/tex]
P(6,3) = 120
There are 120 ways six letters of ALGORITHM be written in a row with first three letters THM.
