(D) Total number of ways to select $2$ horses out of $5$ is given by $^5C_2 = \frac{5 \times 4}{2 \times 1} = 10$.There is only $1$ winning horse. The

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(D) Total number of ways to select $2$ horses out of $5$ is given by $^5C_2 = \frac{5 \times 4}{2 \times 1} = 10$.There is only $1$ winning horse. The number of ways to select $2$ horses such that the winning horse is included is equivalent to choosing the winning horse and one other horse from the remaining $4$ horses,which is $^4C_1 = 4$.Therefore,the probability that $Mr. A$ selected the winning horse is $\frac{4}{10} = \frac{2}{5}$.

Class 11 Mathematics Probability Permutation and Combination based Probability

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Five horses are in a race. $Mr. A$ selects two of the horses at random and bets on them. The probability that $Mr. A$ selected the winning horse is

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A
$\frac{4}{5}$
B
$\frac{3}{5}$
C
$\frac{1}{5}$
D
$\frac{2}{5}$

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Permutation and Combination based Probability

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$A$. Probability that none of the balls is white	$I$. $\frac{1}{70}$
$B$. Probability of getting $2$ white and $1$ blue ball	$II$. $\frac{6}{35}$
$C$. Probability of getting $2$ blue and $1$ white ball	$III$. $\frac{13}{20}$
$D$. Probability of getting $1$ red,$1$ white and $1$ blue ball	$IV$. $\frac{1}{10}$

Five horses are in a race. $Mr. A$ selects two of the horses at random and bets on them. The probability that $Mr. A$ selected the winning horse is

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