In how many ways can a committee consisting of one or more members be formed out of 12 members of Mu

English

Gujarati

Hindi

6.Permutation and Combination

medium

In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation

A

$4095$

B

$5095$

C

$4905$

D

$4090$

Solution

(a) Required number of ways

${ = ^{12}}{C_1}{ + ^{12}}{C_2}{ + ^{12}}{C_3} + …….{ + ^{12}}{C_{12}} = {2^{12}} – 1$

$ = 4096 – 1 = 4095$.

Standard 11

Mathematics

Share

Similar Questions

$^{47}{C_4} + \mathop \sum \limits_{r = 1}^5 {}^{52 – r}{C_3} = $

medium

(IIT-1980)

The number of four letter words that can be formed using the letters of the word $BARRACK$ is

hard

(JEE MAIN-2018)

Each of the $10$ letters $A,H,I,M,O,T,U,V,W$ and $X$ appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letters computer passwords can be formed (no repetition allowed) with at least one symmetric letter ?

normal

From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

hard

(AIEEE-2009)

A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least $3$ girls $?$

medium