Hello everyone, I am having a tricky question. Hopefully, you can help me do it. Thanks a lot.
Question: How many words can be made from 5 letters if all letters are different but 2 particular letters cannot be adjacent?

 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

hello :

70y^8 + 30y^6 = 2 ( 35 y^8 + 15y^6)

the lenght is : 35 y^8

the width is : 15y^6