Question

We must form a bouquet from 18 different flowers so that it should contain not less than three flowers. How many different ways are there of forming such a bouquet?

Answer 1

Number of different ways of selecting flowers to form bouquet

$=C_3^{18}+C_4^{18}+C_5^{18}+C_6^{18}+C_7^{18}+C_8^{18}+C_9^{18}+C_{10}^{18}+C_{11}^{18}+C_{12}^{18}+C_{13}^{18}+C_{14}^{18}+C_{15}^{18}+C_{16}^{18}+C_{17}^{18}+C_{18}^{18}=257924+4048=261972$ ways$.$