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The number of ways 7 different books can be stacked on a shelf is the same as the number of permutations of 7 things taken 7 at a time, which is 7 factorial, or 5040.
7*7 + 7 - 7 is one of many ways to do this.
7! = 5040 ways.
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.