$4$ cards are drawn from a well-shuffled deck of $52$ cards. What is the probability of obtaining $3$ diamonds and one spade?
$4$ cards are drawn from a well-shuffled deck of $52$ cards. What is the probability of obtaining $3$ diamonds and one spade?
Number of ways of drawing $4$ cards from $52$ cards $=^{52} C_{4}$
In a deck of $52$ cards, there are $13$ diamonds and $13$ spades.
$\therefore$ Number of ways of drawing $3$ diamonds and one spade $=^{13} C_{3} \times^{13} C_{1}$
Thus, the probability of obtaining $3$ diamonds and one spade $ = \frac{{^{13}{C_3}{ \times ^{13}}{C_1}}}{{^5{C_4}}}$
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