Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order. From how many different passwords can Will choose?

Answer Choices

Correct answer marked below

390

2,340

4,680

7,020

Correct

14,040

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Explanation

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Official Explanation

Official

Take the task of creating a password and break it into stages.

Stage 1: Select the one letter to be used in the code

There are 26 letters from which to choose, so we can complete this stage in 26 ways.

Stage 2: Select the two digits to be used in the code

Since the order in which we select the two digits does not matter, we can use combinations. We can select 2 digits from 10 digits in

_{10}C_{2}

ways (45 ways). So we can complete stage 2 in 45 ways.

NOTE: We now have the 3 characters to be used in the code. At this point, we need to arrange those 3 characters.…

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What this question tests

What it tests

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

Common trap

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