The number of ways to select one or more book | vedclass

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

Question

(B) The total number of ways to select any number of books (including zero) from $n$ distinct books is given by the sum of combinations: $\binom{n}{0}

Vedclass · Accepted Answer

$63$

Vedclass · Answer

(B) The total number of ways to select any number of books (including zero) from $n$ distinct books is given by the sum of combinations: $\binom{n}{0} + \binom{n}{1} + \binom{n}{2} + \dots + \binom{n}{n} = 2^n$.To select one or more books,we must exclude the case where zero books are selected (i.e.,$\binom{n}{0} = 1$).Therefore,the number of ways to select one or more books from $n$ books is $2^n - 1$.For $n = 6$,the number of ways is $2^6 - 1 = 64 - 1 = 63$.

The number of ways to select one or more books from $6$ books is:

Similar Questions

$A$ boy needs to select five courses from $12$ available courses,out of which $5$ courses are language courses. If he can choose at most two language courses,then the number of ways he can choose five courses is

From a group of $10$ men and $8$ women,the number of ways of forming a committee of $8$ members with not more than $5$ men and not less than $5$ women is

The value of ${}^{50}C_4 + \sum_{r=1}^{6} {}^{56-r}C_3$ is

In an election,the number of candidates is $1$ greater than the persons to be elected. If a voter can vote in $254$ ways,then the number of candidates is:

$n$ balls each of weight $w$. When weighed in pairs,the sum of the weights of all possible pairs is $120$. When they are weighed in triplets,the sum of the weights of all possible triplets is $480$. Then $n$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module