How many permutations of the letters ABCDEFGHI are there...
- That end with any letter other than C.
- That contain the string HI
- That contain the string ACD
- That contain the strings AB, DE and GH
- If letter A is somewhere to the left of letter E
- If letter A is somewhere to the left of letter E and there is exactly one letter between A and E
Total number of permutations - Permutations where the letter ends in C:
9! - 8! = 322560
Treat "HI" as singular letter and calculate permutation as usual:
8! = 40320
Treat "ACD" as singular letter:
7! = 5040
Treat "AB", "DE", "GH" as singular letter:
6! = 720
Question 5, 6
This is where I hit a wall. How do I know the position of A in relation to B? I feel that I won't understand the answer even if I see it.
Is my answer to Q1 - Q4 correct? What is the key to solving Q5 and Q6?