I heard this problem explained on the radio today and was wondering if anyone could work out the answer.

You have an 6 slot egg box with 3 eggs in it, what are the number of possible

combinations you can put the eggs inside, without removing any eggs from the box ( and all the eggs being identical, so basically each slot can either have an egg in it or not).

I'm not very good at maths but my first thought was to try doing 2 to the power of 6, then I realised there was only 3 eggs so not every slot can be filled with eggs so that wouldn't work. I then started thinking of it kind of like a 6 digit binary number, but with the limit that it must always have 3 zeroes in it ( because 3 slots will always be empty).

In the end i kind of thought that the number was obviously below 64 but definitely above 27, and thats about as far as i could get with it.

An answer would be greatly appreciated!