Question 17109 – NTA UGC NET JUNE-2023 Paper-2

To find the sum of all four-digit numbers formed using the digits 1, 2, 4, and 6, you can calculate the sum of each possible permutation and then add them together. There are 24 (4 factorial) permutations of these four digits.

Let’s calculate the sum:

Sum of permutations starting with 1:

1246 + 1264 + 1426 + 1462 + 1624 + 1642 = 8,664
Sum of permutations starting with 2:

2146 + 2164 + 2416 + 2461 + 2614 + 2641 = 14,442
Sum of permutations starting with 4:

4126 + 4162 + 4216 + 4261 + 4612 + 4621 = 25,998
Sum of permutations starting with 6:

6124 + 6142 + 6214 + 6241 + 6412 + 6421 = 37,554
Now, add the sums from all these groups:

8,664 + 14,442 + 25,998 + 37,554 = 86,658