Answer: 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
