(A) The total number of ways to select $2$ cards from a deck of $52$ cards is given by $n(S) = \binom{52}{2} = \frac{52 \times 51}{2 \times 1} = 1326$

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(A) The total number of ways to select $2$ cards from a deck of $52$ cards is given by $n(S) = \binom{52}{2} = \frac{52 \times 51}{2 \times 1} = 1326$. There are $4$ kings in a deck. The number of ways to select $2$ kings from $4$ is $n(E) = \binom{4}{2} = \frac{4 \times 3}{2 \times 1} = 6$. The probability $P(E)$ that both cards are kings is $\frac{n(E)}{n(S)} = \frac{6}{1326} = \frac{1}{221}$.

Class 11 Mathematics Probability Permutation and Combination based Probability

Easy

In a well-shuffled deck of $52$ cards,if two cards are drawn at random,what is the probability that both cards are kings?

A
$\frac{1}{221}$
B
$\frac{5}{221}$
C
$\frac{4}{13}$
D
$\frac{1}{21}$

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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	$(iv)$ $\frac{3}{11}$
	$(v)$ $\frac{9}{110}$

In a well-shuffled deck of $52$ cards,if two cards are drawn at random,what is the probability that both cards are kings?

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