Invitation Problem Here is the question- How many ways you can invite your 7 friends? Here is the answer- For each one, there are two options either you invite them or not. So that gives 2^7 options. But here is the twist. The answer is (2^7)-1. Figure out why! link
Combi Thoughts Here is the question- 1257 is a number where 1<2<5<7. Now the question is how many four digit numbers are there that satisfies this property? The answer- It's really a simple one. Don't think for the order first. Let me explain. See, if you take any four digits you will find that they are always in a order. So it makes sense that you only have to find four digits from the nine digits & that is 9C4.