Question: I was asked to find the four colour stripes of a 1M ohm (tolerance of 5%)

My question now is don't we have 2 options? I came up with:

* Black(0) Brown(1) Blue(x1M) Gold (5%)
* Brown(1) Black(0) Green(x100K) Gold(5%)

Is there one right and one wrong or are both of these correct?

Answer: 
You are not allowed to start with black except for zero ohm jumper, so only your second suggestion is valid.
What if you wanted the colours of a 1.5 Mohm resistor? Your first option doesn't give any ability to specify a 2nd digit so clearly it is a bad choice. The second option allows colours of brown, green and green meaning 15 x 100 kohm.