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Question

A man has $$5$$ friends. In how many ways can he invite one or more of them to a tea party?


A
30
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B
31
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C
32
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D
25
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Solution

The correct option is A $$31$$
First of all calculate the total number of ways in which the friends can be invited i.e without imposing any condition on the number of friends that can come.
Each friend has 2 ways i.e the friend will be invited or the friend will not be invited and also that whether the friend will be invited or not does depend on anybody else so invitation of each friend is an independent event.
So 1 friend leads to  2 ways 
then 5 friends leads to $$ 2\times 2\times 2 \times 2 \times 2 =2^5$$ ways .
Now the condition is one or more friend has to be invited so if we subtract the case where 0 friends were invited from a total number of ways we will get the desired answer.
No. of ways in which no friends are invited $$= 1$$
So our answer is $$= 2^5 -1 = 31$$ ways

Maths

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