(A) Total number of socks $= 5 + 4 = 9$.The total number of ways to draw $2$ socks from $9$ is given by ${}^9C_2 = \frac{9 \times 8}{2 \times 1} = 36$

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(A) Total number of socks $= 5 + 4 = 9$.The total number of ways to draw $2$ socks from $9$ is given by ${}^9C_2 = \frac{9 \times 8}{2 \times 1} = 36$.The two socks will match if both are brown or both are blue.Number of ways to choose $2$ brown socks from $5$ is ${}^5C_2 = \frac{5 \times 4}{2 \times 1} = 10$.Number of ways to choose $2$ blue socks from $4$ is ${}^4C_2 = \frac{4 \times 3}{2 \times 1} = 6$.Total favorable outcomes $= 10 + 6 = 16$.Required probability $= \frac{16}{36} = \frac{4}{9}$.

Class 11 Mathematics Probability Advanced Use of permutations and combinations in probability

Medium

$A$ drawer contains $5$ brown socks and $4$ blue socks well mixed. $A$ man reaches the drawer and pulls out $2$ socks at random. What is the probability that they match?

A
$\frac{4}{9}$
B
$\frac{5}{8}$
C
$\frac{5}{9}$
D
$\frac{7}{12}$

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$A$ drawer contains $5$ brown socks and $4$ blue socks well mixed. $A$ man reaches the drawer and pulls out $2$ socks at random. What is the probability that they match?

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