Independence of irrelevant alternatives

Imagine you have a lot of dishes to clean, and you have to choose which one to do first. The independence of irrelevant alternatives means that if you choose to do one dish first, it should not affect which dish you choose to do next. This means that if you choose to do the plates first, it doesn't mean that you then have to wash the frying pan last. You can still choose to wash the pan first, or wash the cups second, or anything you want. So, no matter which dish you choose to do first, it won't affect which dish you have to do next.