Use Only Three Digits!

Probability Level 2

What is number of different seven digit numbers that can be written using only the three digits 1,2 and 3 and with the condition that the digit 2 occurs exactly twice in each number?

Solve more problems like this in my set Combinatorics

{^7P_2} \times 2^{5}

{^7C_2} \times 2^{5}

{^7C_2} \times 5^{2}

None of these

1 solution

Nikhil Ramakrishnan
Mar 15, 2015

First, we select two places out of the seven to put '2' in them by: ${^7C_2}$

Then, in the remaining five places, '1' or '3' can be filled, so there are two ways to fill each of the remaining places. This is given by: $2^{5}$

Therefore, the final answer is: ${^7C_2} \times 2^{5}$

Use Only Three Digits!

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