a ternary digit is either 0 1 or 2 how many sequences of six

a ternary digit is either 0, 1, or 2. how many sequences of six ternary digits contain the digit 2 exactly twice?

Solution

There are 6C2 = 15 ways to choose where to place that two 2\'s.

Now, for the other 4 places, you can choose two ways: 0 or 1. Thus, there are 2*2*2*2 = 16 ways to fill them out.

Thus, there\'s a total of 15*16 = 240 ways [ANSWER]