A ternary digit is either 01 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? (Hint) think about how many ways there are to place the two 2\'s and then how many ways there are to fill in the order digits.

Please show all work and explain your methods.

Solution

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

Meanwhile, for the other 4 digits, they can only be 0 or 1. Thus, there are 2*2*2*2 = 16 ways to fill them out.

Thus, there are 15*16 = 240 sequences. [ANSWER, 240]