Question

Cards are numbered $1$ to $25$. Two cards are drawn one after the other. Find the probability that the number on one card is a multiple of $7$ and on the other is a multiple of $11$

Answer 1

The cards which are multiple of $7$ are $\{7,14,21\}$ and the card numbers which are multiples of $11$ are $\{11,22\}$
$\therefore n\left(s\right){=}^{25}{C}_{2}n\left(A\right){=}^3{C}_1{\times }^2{C}_1$
$\therefore$ Required probability $=\frac{{}^3{C}_1{\times }^2{C}_1}{{}^{25}{C}_2}=\frac{3\times 2}{300}=\frac{6}{300}=\frac{1}{50}$
$\therefore$ the probability of drawing two cards, where one card is a multiple of $7$ and the other is a multiple of $11$ is $\frac{1}{50}$