$n\left(S\right)$ = Total number of ways of drawing 2 cards from 52 cards = ⁵²C₂

Let E = event of getting 1 club and 1 diamond.

We know that there are 13 clubs and 13 diamonds in the total 52 cards.

$Hence, n\left(E\right)$ = Number of ways of drawing one club from 13 and one diamond from 13

= ¹³C₁ × ¹³C₁

$\text{P(E) = }\dfrac{\text{n(E)}}{\text{n(S)}} $= $\dfrac{13_{C_1} \times 13_{C_1}}{52_{C_2}}$

= $\dfrac{13 \times 13}{\left( \dfrac{52 \times 51}{2}\right)}$=$ \dfrac{13 \times 13}{ 26 \times 51}= \dfrac{13}{ 2\times 51}$=$ \dfrac{13}{102}$