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Find the number of ways of inviting atleast one among 6 people to a party?

+1 vote

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.

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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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