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 $=\frac{{}_{}{}^{3}C{}_2\times {}_{}{}^{10}C{}_1}{{}_{}{}^{16}C{}_3}=\frac{3\times 10\times 6}{16\times 15\times 14}=\frac{3}{56}$