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 $= \frac{\_{}^{3}C _{2} \times \_{}^{10}C _{1}}{\_{}^{16}C _{3}} = \frac{3 \times 10 \times 6}{16 \times 15 \times 14} = \frac{3}{56}$