Question

a person has 8 friends the number of ways in which he may invite one or more of them to a dinner is​

Answer 1

Answer:

The number of ways to invite no friends is 1. Thus, the number of ways to invite at least one friend is 2^8 - 1 = 256 - 1 = 255.

Answer 2

Given:

Number of friends=8

To find:

The number of ways in which the person may invite one or more friends

Solution:

The number of ways in which the person may invite one or more friends is 255.

We can find the number by following the given steps-

We know that the number of ways can be obtained by using the concept of combination.

The person has 8 friends and may invite one or more friends.

We know that the number of ways of choosing a person can be obtained by using nCr=n!/r!(n-r)! where n is the total number of friends and r is the number of friends to be invited.

So, the number of ways of inviting one or more friends=8C1+8C2+8C3+8C4+8C5+8C6+8C7+8C8

8C1=8!/1!(7!)=8

8C2=8!/2!(6!)=28

8C3=8!/3!(5!)=56

8C4=8!/4!(4!)=70

8C5=8!/3!(5!)=56

8C6=8!/2!(6!)=28

8C7=8!/1!(7!)=8

8C8=8!/0!(8!)=1

Using the values,

The number of ways of inviting one or more friends=8+28+56+70+56+28+8+1

=255 ways

Therefore, the number of ways in which the person may invite one or more friends is 255.