Question

John has eight friends, in how many ways can he invite one or more of them to dinner?

• A. $256$
• B. $255$
• C. $264$
• D. $272$

Answer 1

The correct option is B $255$

First of all calculate the total number of ways in which the friends can come i.e without imposing any condition on the number of friends that can come.

Each friend has 2 ways i.e the friend will come or the friend will not come and also that whether the friend will come or not, does not depend on anybody else. So, coming of each friend is an independent event.

Now, $1$ friend leads to $2$ ways

Then, $8$ friends leads to $2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=$ $2^8$ 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 total number of ways we will get the desired answer .

No. of ways in which no friend are invited $=1$

So, our answer is $=2^8-1=255$ ways.