Question 8.

The number of 4-digit numbers possible using 1,1,2, and 4 is

$\frac{4!}{2!} = 12$

Number of 1's, 2's and 4's in units digits will be in the ratio 2:1:1, i.e. 6 1's, 3 2's and 3 4's.

Sum = $6(1) + 3(2) + 3(4) = 24$

Similarly, in tens digit, hundreds digit and thousands digit as well.

Therefore, sum = $24 + 24(10) + 24(100) + 24(1000) = 24(1111)$

Mean = $\frac{24(1111)}{12} = 2222$