We start by decrementing/incrementing the largest and second largest random variables by one at a time:

1 + 2 + 3 + 4 + 5 + 6 + 479

1 + 2 + 3 + 4 + 5 + 7 + 478

...

1 + 2 + 3 + 4 + 5 + 242 + 243

We can't go down without repeating. This is 236 cases.

Next, we perform the process on the 2nd largest and third largest random variables by one at a time:

1 + 2 + 3 + 4 + 6 + 241 + 243

1 + 2 + 3 + 4 + 7 + 240 + 243

...

1 + 2 + 3 + 4 + 123 + 124 + 243

This is 118 cases.

Next we perform this operation on the 3rd largest and 4th largest random variables:

1 + 2 + 3 + 5 + 122 + 124 + 243

1 + 2 + 3 + 6 + 121 + 124 + 243

...

1 + 2 + 3 + 63 + 64 + 124 + 243

This is 59 cases.

Next, perform the operation on the 4th and 5th largest random variables:

1 + 2 + 4 + 62 + 64 + 124 + 243

1 + 2 + 5 + 61 + 64 + 124 + 243

...

1 + 2 + 32 + 34 + 64 + 124 + 243

This is 29 cases.

Next, the 5th and 6th largest random variables:

1 + 3 + 31 + 34 + 64 + 124 + 243

...

1 + 16 + 18 + 34 + 64 + 124 + 243

This is 14 cases.

Finally, the 6th and 7th largest random variables:

2 + 15 + 18 + 34 + 64 + 124 + 243

...

8 + 9 + 18 + 34 + 64 + 124 + 243

This is 7 cases.

Therefore, in total, we have 463 different possible sums with 7 random variables satisfying the inequality constrainsts adding to 500.

That is, we have 463 of such strings:

A + B + C + D + E + F + G

By taking (1 choose 1) times (4 choose 2) = 6 we get the number of different combinations given any 7 random numbers. Since we have 463 different sums, then in total, we can select:

6*463 = 2778 sets of 3 numbers that satisfy the given conditions.