I have a combination of 24 words made from 2048 words. I have 21 of these words known and in order. I am missing 3 words that can be placed in any slot from the 24. How can I work out the number of outcomes that I need to try to find these 3 missing words and where they are in the code?
You have 21 words, out of 24. Therefore, 21 of 24 slots are taken, but not necessarily correctly.
There are 2048 possibilities for each word.
The first word can go into one of any 24 positions, therefore 2048*24. The next in any of 23, and the last in any of 22.
This gives you a total of
2048 * 24 * 2048 * 23 * 2048 * 22, or
2048^3 * 24 * 34 * 22.
That's a total of 154,206,505,795,584 possible combinations. While not impossible to compute, at a reasonable rate of 100,000 attempts per second, you'll be able to try them all in just under 50 years.
This task is highly parallelizable, so you could likely cut that down significantly if you can obtain enough hardware. Even simply knowing the locations of the missing words cuts down the brute force time at 100k guesses a second to just under a day.