Answer:72 words
Step-by-step explanation:
The amount of words that can be made from 5 letters where all letters are different e.g house is
5! = 120
Now provided that two particular letters eg us can not be adjacent we can treat this two words as a single letter then we are left with 4 letters
4! = 24
The total ways of arranging the letters keeping this two words together is
2(4!) = 48
5! - 2(4!) = 72
Answer: 72
Step-by-step explanation:
The easiest way for me to solve this is to find the total combinations and then subtract the number of combinations when the particular letters are adjacent.
I chose the letters to be ABCDE where AB cannot be adjacent.
First, find the Total Combinations:
1st letter and 2nd letter and 3rd letter and 4th letter and 5th letter
5 × 4 × 3 × 2 × 1 = 120
Next, find the combinations of AB adjacent (AB or BA):
AB in 1st & 2nd position: AB × 3 × 2 × 1 = 6
AB in 2nd & 3rd position: 3 × AB × 2 × 1 = 6
AB in 3rd & 4th position: 3 × 2 × AB × 1 = 6
AB in 4th & 5th position: 3 × 2 × 1 × AB = 6
TOTAL = 24
Combinations of BA are the same (24)
Now, let's solve.
Total Combinations - Combinations of AB - Combinations of BA
120 - 24 - 24 = 72
