Imagine lining 7 people in a row.
You have 7 people to choose from for the first person and 6 people to choose from for the second person and so on and so on , so
answer=7x6x5x4x3x2x1
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7 factorial, or 5,040.
5040
The letters in the word can be arranged in 7!/4! = 210 ways if A and a are treated the same. If A and a are considered different (so that, for example, Alabama is not alabAma), then there are 7!/3! = 840 ways.
ANS 420 problem 7!/ (6!*2!)
8! or 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320