When 1 Coulomb charge flow through a wire in 1 second then the current through the wire is 1 AMPERE.
I=Q/t
1 Ampere = 1 Coulomb /1 Second
Charge on 1 electron = 1.6 x 10^-19 Coulomb
By unitary method,
If 1.6 x 10^-19 Coulomb / Second (Ampere) = Current by 1 electron
then, 1( Coulomb / Second) or (Ampere) = 1 / (1.6 x 10^-19) electrons
i.e, 6.25 x 10^18 electrons.