Question

Suppose we want to form three-digit numbers using the set of digits (0,1,2,3,4,5). For example, 301 and 223 are such numbers, but 037 is not. How many such numbers are possible? There are three-digit numbers formed by using the digits {0,1,2,3,4,5).

Answer 1

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We have _ _ _ (3 blanks) for each possible number.

Now in the first blank, we can put 1, 2, 3, 4 or 5 i.e. 5 possible numbers can put in first blank.

We cannot put 0 in the first blank, cause that wouldn't generate 3 digit number.

Hence, we have 5 _ _.

Now for the second and third blank, we can put any of the six numbers(0, 1, 2, 3, 4 or 5) i.e. 6 possible numbers

Hence, we have 5 6 6 = 5 x 6 x 6 = 180(3-digit) possible numbers.

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