(D) Total number of cards $= 52$.Total number of kings in a deck $= 4$.The number of ways to choose $2$ cards out of $52$ is given by $^{52}C_2 = \fra

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(D) Total number of cards $= 52$.Total number of kings in a deck $= 4$.The number of ways to choose $2$ cards out of $52$ is given by $^{52}C_2 = \frac{52 \times 51}{2 \times 1} = 1326$.The number of ways to choose $2$ kings out of $4$ is given by $^4C_2 = \frac{4 \times 3}{2 \times 1} = 6$.Therefore,the probability that both cards are kings is $P = \frac{^4C_2}{^{52}C_2} = \frac{6}{1326} = \frac{1}{221}$.

Class 11 Mathematics Probability Permutation and Combination based Probability

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From a well-shuffled pack of $52$ cards,two cards are drawn at random. The probability that both cards are kings is:

AP EAMCET 2022 All AP EAMCET

A
$\frac{1}{15}$
B
$\frac{25}{57}$
C
$\frac{35}{256}$
D
$\frac{1}{221}$

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$A$ bag contains $4$ red,$3$ white,and $5$ blue balls. Three balls are drawn at a time randomly from the bag. Match the items from List-$I$ with those of List-$II$.
List-$I$ List-$II$
$A$. Probability of getting $1$ red,$1$ white and $1$ blue ball $(i)$ $\frac{3}{44}$
$B$. Probability of getting $2$ white and $1$ blue ball $(ii)$ $\frac{21}{55}$
$C$. Probability of getting $2$ red and $1$ white ball $(iii)$ $\frac{38}{55}$
$D$. Probability that none of the balls is white $(iv)$ $\frac{3}{11}$
$(v)$ $\frac{9}{110}$

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List-$I$	List-$II$
$A$. Probability of getting $1$ red,$1$ white and $1$ blue ball	$(i)$ $\frac{3}{44}$
$B$. Probability of getting $2$ white and $1$ blue ball	$(ii)$ $\frac{21}{55}$
$C$. Probability of getting $2$ red and $1$ white ball	$(iii)$ $\frac{38}{55}$
$D$. Probability that none of the balls is white	$(iv)$ $\frac{3}{11}$
	$(v)$ $\frac{9}{110}$

From a well-shuffled pack of $52$ cards,two cards are drawn at random. The probability that both cards are kings is:

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