Chances someone has an ace (or any other holding)

[Joost1982]

Thanks for the calculations!

[AngusThermopyle]

When the probabilities are small, adding them together (which is what multiplying by 6 is doing) does not introduce significant errors, so it suffices for ballpark computations.

When the probabilities are large, you can see where there are problems.

Six handed game:
Odds a specific player is suited: 12/51 , or around 24%.
Using your method to find odds that at least one player is suited would give around 6*24 = 144%, which is clearly false.