Question

A and B draw two cards each, one after another, from a pack of well-shuffled pack of 52 cards. The probability that all the four cards drawn are of the same suit is
(a) $\frac{44}{85\times 49}$

(b) $\frac{11}{85\times 49}$

(c) $\frac{13\times 24}{17\times 25\times 49}$

(d) none of these

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right)\frac{44}{85\times 49} \\ \text{Total cards}=52 \\ \text{There are four suits of cards in a pack, i.e. diamond, heart, spade and club.} \\ P\left(\text{all 4 cards are of same suit}\right)=P\left(\text{all 4 cards are of diamond}\right)+P\left(\text{all 4 cards are of heart}\right)+P\left(\text{all 4 cards are of spade}\right)+P\left(\text{all 4 cards are of club}\right) \\ =4\times \frac{13}{52}\times \frac{12}{51}\times \frac{11}{50}\times \frac{10}{49} \\ =4\times \frac{11}{85\times 49} \\ =\frac{44}{85\times 49} \end{gathered}$$