A man has 7 friends. In how many ways can he | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For each of the $7$ friends,the man has $2$ choices: either to invite them or not to invite them.Since there are $7$ friends,the total number of w

Vedclass · Accepted Answer

$127$

Vedclass · Answer

(C) For each of the $7$ friends,the man has $2$ choices: either to invite them or not to invite them.Since there are $7$ friends,the total number of ways to invite any number of friends (including the case where no one is invited) is $2^7 = 128$.However,the question specifies that he must invite 'one or more' friends,which means we must exclude the case where no friend is invited.The number of ways to invite no friends is $^7C_0 = 1$.Therefore,the required number of ways is $2^7 - 1 = 128 - 1 = 127$.

$A$ man has $7$ friends. In how many ways can he invite one or more of them for a tea party?

Similar Questions

The number of triangles that can be formed by choosing the vertices from a set of $12$ points,$7$ of which lie on the same straight line,is

$^{14}C_4 + \sum_{j=1}^4 {^{18-j}C_3}$ is equal to

How many $3$-digit numbers,each less than $600$,can be formed from the digits $1, 2, 3, 4, 5,$ and $9$,if repetition of digits is allowed?

The number of words which can be made out of the letters of the word $MOBILE$ when consonants always occupy odd places is

The number of numbers between $2,000$ and $5,000$ that can be formed using the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) which are multiples of $3$ is?

Vedclass Test Series

Exam Paper Generator

Online Exam Module