a) No condition is imposed
We can use any of the seven letters in each position...so
7 * 7 * 7 * 7 = 2401 "words"
b) No letter can be repeated in a word.
We have 7 ways to pick the first letter, 6 ways to pick the second, 5 ways to pick the third and 4 ways to pick the fourth............so 7 * 6 * 5 * 4 = 840 "words"
c) Each word must begin with the letter A
If we can repeat letters, the other three positions can be filled in 7 * 7 * 7 = 343 ways....so..we have 343 "words"
If we cannot repeat letters we have 6 * 5 * 4 ways to fill the other three positions = 120 "words"
d) The letter C must be at the end.
Same answers as (c)
e) The second letter must be a vowel.
If we can repeat letters....we have 7 ways to fill three of the positions and 2 ways to fill the remaining one [ since we have only two vowels ]...so.... 7 * 2 * 7 * 7 = 686 "words"
If we cannot repeat letters, we have 7 * 2 * 6 * 5 = 420 "words"
