Q.Two cards are drawn from a pack of 52 cards. Find the probability that a) one is a face card and the other is an ace card b) one is club and the other is a diamond c) both are from the same suit d) both are red cards e) one is a heart card and the other is a non heart card.

$n(S)=\binom{52}{2}=1326$.

a) One face card (12 total), one ace (4 total): $12\times4=48$, $P=48/1326=8/221$.

b) One club (13), one diamond (13): $13\times13=169$, $P=169/1326=13/102$.

c) Both same suit: $4\times\binom{13}{2}=4\times78=312$, $P=312/1326=4/17$.

d) Both red: $\binom{26}{2}=325$, $P=325/1326=25/102$. …

Treat the two cards as an unordered pair, use $n(S)=\binom{52}{2}$, and count favourable combinations by multiplying …

Using $52\times51$ (ordered) for $n(S)$ while counting favourable outcomes as unordered combinations, mixing the two c …