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Answer :
Final answer:
One would apply permutations without repetition in this problem, using the formula nPr = n! / (n-r)! After applying numbers to the formula (where n=7 and r=6), the correct answer would be 5040 passwords.
Explanation:
This is a problem of permutations. Permutations are the number of ways you can arrange a certain number of items when the order of those items matters. In this case, we have 7 letters (a, b, c, d, e, f, g) and we want to arrange 6 of them with no repetition. We use the formula for permutations without repetition, which is nPr = n! / (n-r)!. For this problem, n=7 (the total number of letters) and r=6 (the total number of letters in the password). So the solution is 7P6 = 7! / (7-6)! = 7*6*5*4*3*2*1 / 1 = 5040. Therefore, there are 5040 different 6-letter passwords that can be made from these letters with no repetition.
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