Question

in how many different ways can the digit 0 to 5 be arranged three at a time?

Answer 1

You have 3 places to fill with 6 different digits (0, 1, 2, 3, 4, 5. that's 6 different numbers).

As the duplication of digits is not allowed, there are 6 possible first digits, 5 possible second digits, and 4 possible third digits. Thus, the number of different ways that the digit 0 to 5 be arranged three at a time are (6 × 5 × 4) = 120.

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Alternatively, this represents the number of permutations of 6 things taken 3 at a time. Thus, the number of different ways that the digit 0 to 5 be arranged three at a time are 6P3 = 6!/(6-3)! = 6!/3! = 6 × 5 × 4 = 120.