You use what is called the factorial if a number – written (for the number 3) as 3! The value is the number multiplied by every integer below it = 3x2x1 = 6 for “3!”. Excel has a function fact(x) to do this

The number of Permutations of x soldiers in a froup of N soldiers is N!/(x!)(N-x)! or 100!/(3! x 97!) – work it out.

If the order is important such as they take it in turns to be in charge and you want the number of patrols with unique patrol leaders then the formula is N!/(N-x)! or 100!/97!

III three at a time

Unless the hundred lose their place in line it will never happen in a strait line.

This is the same as a combination lock. Only you have a hundred numbers and 3 possible combinations. I think that has 30000 possibilities. I am not sure though it may be 3000.

To solve this you will need to take one guy and concentrate on him and get everyone with him, then move on to the next guy, so every guy will have to share 50 nights on watch so the hundred would be times 50 giving you 500 possible nights on watch.