Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is-

Answer: Option D

Let S be the sample space.
Then, n(S) = $${}^{52}{C}_2$$  $$=\frac{\left(52\times 51\right)}{\left(2\times 1\right)}$$   = 1326
Let E = event of getting 1 spade and 1 heart.
∴ n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13
$$=\left({}^{13}{C}_1\times {}^{13}{C}_1\right)$$   = (13 × 13) = 169
$$\therefore P(E)=\frac{n(E)}{n(S)}=\frac{169}{1326}=\frac{13}{102}$$