From a well shuffled pack of $52$ playing cards, four are drawn at random. The probability that all are spades, but one is a king is:

\frac{^{39} C_{4}}{^{52} C_{4}}

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\frac{^{12} C_{3}}{^{52} C_{4}}

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- \frac{^{39} C_{4}}{^{52} C_{4}}

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\frac{^{12} C_{4}}{^{52} C_{4}}

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Solution

The correct option is B $\frac{^{12} C_{3}}{^{52} C_{4}}$
Total No. Of cards $= 52$
Total cards of spade $= 13$
$P r o b a b i l i t y = \frac{C o n d i t i o n a l c a s e}{t o t a l c a s e}$

So,
Total no. Of conditional case of drawing $4$ cards of spade but one is king $=$ no. of case of selecting all four cards of spade suit
$=^{12} C_{3} \times 1$
Total no. of case $=^{52} C_{4}$
Probability of being one card as king out of four $= \frac{^{12} C_{3}}{^{52} C_{4}}$

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Similar questions

^{47} C_{4} + \sum_{j = 1}^{5}^{52 - j} C_{3} =

Question 52
Under what conditions are $C_{4}$ plants superior to $C_{3}$ ?

^{47} C_{4} + 5 \sum r = 1^{52 - r} C_{3}

52

52

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