Students are often troubled with combinatorics questions. TMost of them have never been given a proper explanation for the formulas for combination, variation, and permutation.

In the given problem we are looking for all numbers which:

1) Have three digits

2) The first digit is a number multiple of 3.

3) The number is a multiple of 2.

The best way I know to solve this problem is by drawing 3 squares in a row. Each square represents a digit of the number which is hidden behind it.

Which digits could be written behind the first square? 3, 6, and 9

Which digits could be written behind the second square? All 10 digits

Which digits could be written behind the third square? 0, 2, 4, 6, 8

Now fill each square with the amount of digits which fit the description of the problem. The scetch would look like this: |3|10|5|. Now we multiply these numbers to get the answer of the question -> 3105=150

Normally, this type of questions is firstly explained with super easy examples so that the student can see, for example, why at the end the 3 numbers should be multiplied.

Factorize 9x+3xy-9zyx

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