The number of ways to select n objects from 2 | vedclass

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

Question

(A) We need to select $n$ objects from $2n$ objects,where $n$ objects are identical and $n$ objects are distinct.Let $k$ be the number of distinct obj

Vedclass · Accepted Answer

$2^{n}$

Vedclass · Answer

(A) We need to select $n$ objects from $2n$ objects,where $n$ objects are identical and $n$ objects are distinct.Let $k$ be the number of distinct objects selected,where $0 \le k \le n$.Then the remaining $(n-k)$ objects must be selected from the $n$ identical objects.Since the $n$ identical objects are indistinguishable,there is only $1$ way to select any number of them.Thus,for each $k$ from $0$ to $n$,the number of ways to select $k$ distinct objects is given by $\binom{n}{k}$.The total number of ways is the sum of these possibilities:$\sum_{k=0}^{n} \binom{n}{k} = \binom{n}{0} + \binom{n}{1} + \binom{n}{2} + \dots + \binom{n}{n} = 2^{n}$.

The number of ways to select $n$ objects from $2n$ objects,of which $n$ are identical and the rest are different,is:

Similar Questions

$^nC_r + ^{n-1}C_r + ...... + ^rC_r =$

$A$ student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first $5$ questions. The number of choices available to him is

The number of ways in which a committee of $6$ members can be formed from $8$ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is

Out of $13$ cricket players,$4$ are bowlers. In how many ways can a team of $11$ players be selected such that the team contains at least $2$ bowlers?

In how many ways can one select a cricket team of $11$ from $17$ players in which only $5$ players can bowl,if each cricket team of $11$ must include exactly $4$ bowlers?

Vedclass Test Series

Exam Paper Generator

Online Exam Module