4 cards are drawn from a well-shuffled deck of 52 cards. probability of obtaining 3 diamonds and one

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14.Probability

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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?

A

$ \frac{{^{13}{C_3}{ \times ^{13}}{C_1}}}{{^5{C_4}}}$

B

$ \frac{{^{13}{C_3}{ \times ^{13}}{C_1}}}{{^5{C_4}}}$

C

$ \frac{{^{13}{C_3}{ \times ^{13}}{C_1}}}{{^5{C_4}}}$

D

$ \frac{{^{13}{C_3}{ \times ^{13}}{C_1}}}{{^5{C_4}}}$

Solution

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}}}$

Standard 11

Mathematics

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