Question

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?

Answer 1

Explanation:

a.362880 b.40320. c.720

Answer 2

Answer: a) 362880 b) 40320 c)720

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