Splitting water supply to fridge

Hi
Im interested in ordering an Admiral with a water cooler and ice maker.
I have a washing machine point in the kitchen which I want to split to get the water to where the fridge will be about 3m away (ends in standard blue plastic female connector).
I have bougth a Y piece connector (one female, to two male) and a extra length of pipe (with 2 female ends) , but I cant figure out how I will also attach the washing machine. I think I need a extra male-male connector to get everything to work properly.
Is it actually possible to split the water supply in this way? Can anyone give me some tips please.

Jon