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A 5-place PIN is formed using the digits 0, 1, 2, 3, 4, and 5. The first two places must contain different digits, and the last digit must differ from the first. Repetition is allowed in all other places. How many PINs are possible?

Answer and explanation

Correct answer: 5400 PINs

The first place has 6 choices. The second has 5 choices because it must differ from the first. Each of the two middle places has 6 choices, and the last has 5 choices because it must differ from the first. Thus, the total is 6 × 5 × 6 × 6 × 5 = 5400 PINs.

Related tags

Counting PrinciplePermutationsClass 11Fundamental Principle Of CountingPermutations And CombinationsMathematicsClass 11 Mcq

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