Question

A showroom has 10 different pairs of expensive shoes. A thief steals 4 shoes randomly from the showroom.
Match the following:
$\begin{array}{cccc}& Column-I& & ColumnII\\ \left(a\right)& Theprobabilitythatthereisno& \left(p\right)& \frac{3}{19\times 17}\\ & matchingpairamongthe4shoesstolenis& & \\ \left(b\right)& Theprobabilitythatthereisatleastone& \left(q\right)& \frac{16}{19\times 17}\\ & matchingpairamongthe4shoesstolenis& & \\ \left(c\right)& Theprobabilitythatthereisexactlyone& \left(r\right)& \frac{{}^{20}{C}_4{-}^{{}^{10}{C}_4{.2}^4}}{{}^{20}{C}_4}\\ & matchingpairamongthe4shoesstolenis& & \\ \left(d\right)& Theprobabilitythattherearetwomatching& \left(s\right)& \frac{14\times 16}{19\times 17}\\ & pairsamongthe4shoesstolenis& & \\ & & \left(t\right)& \frac{98}{19\times 103}\end{array}$

• A. (A) $\to$ (s) (B) $\to$ (r) (C) $\to$ (q) (D) $\to$ (p)
• B. (A) $\to$ (q) (B) $\to$ (s) (C) $\to$ (p) (D) $\to$ (r)
• C. (A) $\to$ (r) (B) $\to$ (s) (C) $\to$ (p) (D) $\to$ (q)
• D. (A) $\to$ (s) (B) $\to$ (r) (C) $\to$ (t) (D) $\to$ (p)

Answer 1

The correct option is A (A) $\to$ (s) (B) $\to$ (r) (C) $\to$ (q) (D) $\to$ (p)

(a) $\frac{20\times 18\times 16\times 14}{20\times 19\times 18\times 17}=\frac{14\times 16}{19\times 17}$
(b) $1-p=1-\frac{{}^{10}{C}_4\times 24}{{}^{20}{c}_4}=\frac{1-14\times 16}{19\times 17}$
(C) Selecting 1 pair of 10, and no matching among the other $=\frac{16}{19\times 17}$
(d) $\frac{{}^{10}{C}_2}{{}^{20}{C}_4}=\frac{3}{19\times 17}$