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

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

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Total number of ways of drawing 4 cards from a deck of 52 cards = ^{52}\textrm{C}_{4}

We know that there are 13 diamonds and 13 spades in a deck.

Now, Number of ways of drawing 3 diamonds and 1 spade = ^{13}\textrm{C}_{3}.^{13}\textrm{C}_{1}

\therefore Probability of obtaining 3 diamonds and 1 spade

= \frac{^{13}\textrm{C}_{3}.^{13}\textrm{C}_{1}}{^{52}\textrm{C}_{4}}

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