Permutation and Combinations — Maths STD 11 Science — Question

The number of numbers beginning with $1=\frac{6 !}{3 ! 2 !}=\frac{4 \times 5 \times 6}{2}=60$, as when 1 is
fixed at the extreme left position, the remaining digits to be rearranged will be 0, 2, 2, 2, 4, 4, in which there are 3, 2 s and 2, 4 s
Total numbers begining with 2
= $\frac{6 !}{2 ! 2 !}=\frac{3 \times 4 \times 5 \times 6}{2}=180$
and total numbers begining with $4=\frac{6 !}{3 !}=4 \times 5 \times 6=120$
Thus,the required number of numbers = 60 + 180 + 120 = 360