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  ______?
asked Jun 24 in Discrete Maths by gbeditor (44,490 points)
reshown 6 days ago by gbeditor

1 Answer

+2 votes
 
Best answer

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 deepak-gatebook (112,390 points)
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