Question

A bouquet from from 11 different flowers is to be made so that it contains not less than three flowers then the number of different ways of selecting flowers to form the Bouquet​

Answer 1

$\huge\star{\tt{\underline{\underline{\red{Answer\implies1981}}}}}\star$

Given: Atleast 3 flowers need to be selected

So selection of flowers of a total of 11 flowers is

$\implies$ $\large{^{11}C_{3}}$

Also We know that we can select more than just three flowers

so selection will be

$\large{^{11}C_{3} + ^{11}C_{4} + ^{11}C_{5}+^{11}C_{6}+^{11}C_{7}+^{11}C_{8}+^{11}C_{9}+^{11}C_{10}\\ \\+^{11}C_{11}}$

$\implies$ 165 + 330 + 462 + 462 + 330 +165 + 55 + 11 + 1

$\implies$ $\large{\boxed{\boxed{1981}}}$

Answer 2

For selection of Flowers

Minimum to be selected are 3 but we can select more than 3 flower from total of 11 flowers

So Selection of Three flowers will be $^{11}C_{3}$

similarly selection for others will be $^{11}C_{4} ,^{11}C_{5} .......^{11}C_{11}$

so all ill be added

$\implies$$^{11}C_{3} +^{11}C_{4} +^{11}C_{5} </p><p>+^{11}C_{6} +^{11}C_{7} +^{11}C_{8} \\ \\+^{11}C_{9} +^{11}C_{10} +^{11}C_{11}$

$\implies$ 1981