How many ways can six of the letters of the word ALGORITHM b

How many ways can six of the letters of the word ALGORITHM be selected and written in a row? How many ways can the letters of the word ALGORITHM be arranged in a row if the letters GOR must remain together (in this order)?

Solution

In ALGORITHM, there letters are all distinct.

Thus, the number of ways to permute n distinct object is n!

Here, there n = 9 letters.

Thus,

#ways = 9! = 362880 [answer]

****************************

If we put GOR together in that order, we can treat them as just 1 object.

Thus, it\'s like there are now just 7 objects: A,L,GOR,I,T,H,M.

Thus, there are

#ways = 7! = 5040 [answer]