If five digit numbers are formed from the digits $0,1,2,3$, 4 using every digit exactly only once, then the…
If five digit numbers are formed from the digits $0,1,2,3$, 4 using every digit exactly only once, then the probability that a randomly chosen number from those numbers is divisible by 4 , is
$\frac{5}{16}$
$\frac{3}{16}$
$\frac{3}{8}$
$\frac{7}{16}$
Solution
Total number of five digits number $=4 \cdot 4 \cdot 3 \cdot 2.1=96$
For number divisible by 4 contain
Last two digit $04=3!=6$
Last two digit $40=3!=6$
Last two digit $20=3!=6$
Last two digit $12=2.2!=4$
Last two digit $32=2.2!=4$
Last two digit $24=2.2!=4$
$\therefore$ Total number divisible by 4
$=6+6+6+4+4+4=30$
Required probability $=\frac{30}{96}=\frac{5}{16}$