# DM - Functions & Relations -Q20

+1 vote
A set contains 21  elements. The number of subsets of this set containing more than 10 elements is equal to  ______?
reshown 6 days ago

A set contains 21  elements. The number of subsets of this set containing more than 10 elements :

$\binom{21}{11} + \binom{21}{12} + \dots \binom{21}{21}$

NOTE that :

$\binom{n}{r} = \binom{n}{n-r}$

So,

$\binom{21}{11} + \binom{21}{12} + \dots \binom{21}{21} = \binom{21}{10} + \binom{21}{9} + \dots \binom{21}{0}$

We know that $\binom{21}{0} + \binom{21}{1} + \dots +\binom{21}{21} =2^{21}$

So,

$\binom{21}{11} + \binom{21}{12} + \dots \binom{21}{21} = \binom{21}{10} + \binom{21}{9} + \dots \binom{21}{0} = 2^{21}/2$

$2^{20}$

=  1048576

answered 4 days ago by (112,390 points)