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Q.
The sum of all the four digit numbers formed with the digits $0, 1, 2, 3$ taken all at a time is
Permutations and Combinations
Solution:
A four digit number to be formed with digits $0, 1, 2, 3$ taken all at a time. If $1$ will be in units place, we have four such numbers and so $2$ and $3$ will come in unit place four times.
Hence sum in units place $= 4 (1 + 2 + 3) = 24$.
So will the sum be in tens and hundreds place. But in thousands place $1$ will come $6$ times and so the other non-zero digits. Hence sum in thousand's place will be
$= 6 (1 + 2 + 3) = 6 \times 6 = 36$.
Hence, the required sum is
$36 \times 1000 + 24 \times 100 + 24 \times 10 + 24 = 38664$.