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Question: In how many ways can you arrange the letters in the word RANDOM?


A ) 720
B ) 320
C ) 420
D ) 520

Steps to derive

1 Number of possible outcomes for choosing the first letter = 6
 [There are 6 letters in the word.]

2 Number of possible outcomes for choosing the second letter = 5
 [There are 5 letters remaining to choose.]

3 Number of possible outcomes for choosing the third letter = 4
 [There are 4 letters remaining to choose after choosing 2 letters.]

4 Number of possible outcomes for choosing the fourth letter = 3
 [There are 3 letters remaining to choose after choosing 3 letters.]

5 Number of possible outcomes for choosing the fifth letter = 2
 [There are 2 letters remaining to choose after choosing 4 letters.]

6 Number of possible outcomes for choosing the sixth letter = 1
 [There is only 1 letter remaining to choose after choosing 5 letters.]

7 
1st letter       2nd letter       3rd letter       4th letter       5th letter       6th letter
     6         x        5        x        4        x          3        x         2        x        1        =   720
 [Multiply the number of possible outcomes of choosing each letter in the word.]

8 The letters in the word can be arranged in 720 ways.



Hence the right answer is Option A

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