4 cards are drawn from a well-shuffled deck of 52 cards.
Question:

4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?

Solution:

Number of ways of drawing 4 cards from 52 cards $={ }^{52} \mathrm{C}_{4}$

In a deck of 52 cards, there are 13 diamonds and 13 spades.

$\therefore$ Number of ways of drawing 3 diamonds and one spade $={ }^{13} \mathrm{C}_{3} \times{ }^{13} \mathrm{C}_{1}$

Thus, the probability of obtaining 3 diamonds and one spade $=\frac{{ }^{13} \mathrm{C}_{3} \times{ }^{13} \mathrm{C}_{1}}{{ }^{52} \mathrm{C}_{4}}$.

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