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Find the number of ways of inviting atleast one among 6 people to a party?
asked in Quantitative Aptitude by (276 points) 1 7 26 | 59 views

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A person can invite at least 1 people among 6 people in these manners.

  1.  At least 1 people are invited among 6 people. This can be done in 6C1 ways

OR

       2.  2 people can be invited among 6 people. This can be done in 6C2 ways.

OR 

       3.  3 people can be invited among 6 people. This can be done in 6C3 ways

OR

      4.   4 people can be invited among 6 people. This can be done in 6C4 ways.

OR

      5.   5 people can be invited among 6 people. This can be done in 6C5 ways.

OR

      6.   All the 6 people can be invited among 6 people. This can be done in 6C6 ways.

Total number of ways =  6C1 6C2 + 6C36C46C56C6 ways

                                   = 6 + 15 + 20 + 15 + 6+ 1

                                   = 63 ways.

answered by (5.7k points) 7 25 141
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number of ways of inviting atleast one among 6 people to a party

= Total no of ways inviting $ 6$ people $-$Not inviting anyone
$=2^6-1 \\=63$
PS:_ _ _ _ _ _ :$\Rightarrow$ 6 peoples Binary choice $0 \ OR \ 1 \\000000 \rightarrow not  \ inviting\ anyone$

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