A. How many ways can the letters of the word ALGORITHM be arranged in a row? b. How many ways can the letters of the word ALGORITHM be arranged in a row if A and L must remain together (in order) as a unit?
c. How many ways can the letters of the word ALGORITHM be arranged in a row if the letters GOR must remain together (in order) as a unit?

a) 362880   b) 40320  c)720

Step-by-step explanation:

a) There are  9 letters in the word  ALGORITHM. Pls note that all 9 letters are different.

So to find the number of the ways which the letters can be arranged lets imagine , that in 1st place can stay any of 9 letters, in second place any of remaining 8 letters, in 3-rd place - any of 7 letters etc

So total number of the ways is

N= 9*8*7*6*5*4*3*2*1=9!=362880

b) If A and L must remain togetherin order AL ( LA is forbidden !) so we can imagine that AL is 1 special letter.

So total number of the letters is 8. Similarly to a) we can find the number of the ways as:

N=8*7*6*5*4*3*2*1=40320

c) Similarly to b) lets imagine that GOR is 1 special letter. So there are only 7 letters . Similarly to a) the number of the ways is

N=7*6*5*4*3*2=720

sine

step-by-step explanation: