A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour, is

Total number of Socks = 5+4 = 9
The number of ways to Select 2 Socks out of 9 ${=}^9{\mathrm{C}}_2$
Number of ways to select both brown socks = ${=}^5{\mathrm{C}}_2$
And number of ways to select both white socks = ${=}^4{\mathrm{C}}_2$
P(either both brown or white) =$=\frac{{ }^5{\mathrm{C}}_2{+}^4{\mathrm{C}}_2}{{ }^9{\mathrm{C}}_2}$

$=\frac{\frac{5!}{3!\cdot 2!}+\frac{4!}{2!\cdot 2!}}{\frac{9!}{7!\cdot 2!}}=\frac{10+6}{36}=\frac{16}{36}\times \frac{3}{3}=\frac{48}{108}$