There are 100 person and I want to invite at least one then in how many different ways I can invite?

Question

I m very confused from this question last 1 week. Plz help me . How can we solve such type of questions . Plz help . 

Answer 1

you can invite just one person in 100 ways (100C1); 2 persons in 100C2 ways, 3 persons in 100C3 ways, etc, up to inviting everyone, 100C100.  but ruled out is inviting nobody (100C0).

 

add up ALL of these, including the 'nobody' option.  if you know anything about the Pascal Triangle, you will see that this ALL value equals (1+1)¹⁰⁰.

 

therefore the number of ways to do any kind of viable inviting equals 2¹⁰⁰-1.