Question

What is the total number of ways of selecting at least one object from 2 sets of 10 distinctly different?

Answer 1

As there are two sets.. At first one set will be selected.. This selection will take place in 2C1 ways..

Now.. The person will select at least one object from 10 objects..

At least one clearly defines that more than one is permitted and maximum number of object is 10.. And person will select one or more than one object.. As it is connected by or.. We'll use ‘+’

So no. Of ways to select at least one is =

10C1 +10C2+…..+10C9 +10C10

Now..

The person will first select set and then objects..

As the statement is connected by and.. We'll use product

Total no of ways= 2C1(10C1 +10C2+…..+10C9 +10C10)

There's a property..

nc1+ nc2…. nCn = (2^n) -1

Hence,

Total no of ways= 2C1*{(2^10)-1}

2 x 1023 =2046