Explanation

(a)
Since, a five digit number is formed using digits $\{ 0,\ 1,\ 2,\ 3,\ 4\ and\ 5\}$ divisible by 3 $ie$, only possible when sum of digits is multiple of 3 which gives two cases.
Case I {using digits :0, 1, 2, 4, 5}
Number of numbers $= 4 \times 4 \times 3 \times 2 \times 1 = 96$
Case II{using digits 1, 2, 3, 4, 5}
Number of numbers $= 5 \times 4 \times 3 \times 2 \times 1 = 120$
$\therefore$ Total number of formed $120 + 96 = 216$