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  4. Two cards are drawn at random from a pack of 52 cards. The probability of getting at least a spade and an ace, is

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Q. Two cards are drawn at random from a pack of $52$ cards. The probability of getting at least a spade and an ace, is

Bihar CECEBihar CECE 2013

Solution:

Total number of cases, $n(s)=55 C_{2}$
$n(E)=$ The number of selection of $1$ spade, $1$ ace from $3$ aces or selections of the ace of spade and $1$ other spade.
$13 C_{1} \times 13 C_{4}+12 C_{1} \times 11 C_{1}=51$
$\therefore P(E) \frac{51}{52 C_{2}}=\frac{1}{26}$