In how many ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?

Correct answer marked below

720

864

900

936

Correct

1,296

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Explanation

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Official Explanation

Official

Total number of four-letter passwords =

6 \times 6 \times 6 \times 6 = 1296

----- (1)

Total number of passwords in which no letter repeats =

{}_6C_4 \times 4! = 15 \times 24 = 360

----- (2)…

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What this question tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.