Question

A purse contains three $10$ paise, three $50$ paise and ten $1$ rupee coins. If three coins are selected at random, then the probability that the total amount is $2$ rupees is

• A. $\frac{2}{5}$
• B. $\frac{3}{56}$
• C. $\frac{1}{4}$
• D. $\frac{1}{8}$

Answer 1

Answer: (B)

Favourable cases $=$ There is only one possibility as $3$ coins must be two $50$ paise coin and one $1$ rupee coin
Number of favourable ways $=\_{}^3{C}_2\times \_{}^{10}{C}_1$
Total number of ways $=\_{}^{16}{C}_3$
Hence, the required probability $=\frac{\_{}^3{C}_2\times \_{}^{10}{C}_1}{\_{}^{16}{C}_3}=\frac{3\times 10\times 6}{16\times 15\times 14}=\frac{3}{56}$