If m rupee coins and n ten paise coins are pl | vedclass

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

Question

(B) Total number of ways to arrange $m$ rupee coins and $n$ ten paise coins in a line is given by the number of permutations of $m+n$ objects where $m

Vedclass · Accepted Answer

$\frac{n(n - 1)}{(m + n)(m + n - 1)}$

Vedclass · Answer

(B) Total number of ways to arrange $m$ rupee coins and $n$ ten paise coins in a line is given by the number of permutations of $m+n$ objects where $m$ are of one type and $n$ are of another type: $\frac{(m + n)!}{m! n!}$.If the extreme coins are ten paise coins,we fix two ten paise coins at the two ends. The remaining $(m + n - 2)$ coins consist of $m$ rupee coins and $(n - 2)$ ten paise coins.The number of ways to arrange these remaining coins is $\frac{(m + n - 2)!}{m! (n - 2)!}$.Therefore,the required probability is:$P = \frac{\frac{(m + n - 2)!}{m! (n - 2)!}}{\frac{(m + n)!}{m! n!}}$$P = \frac{(m + n - 2)!}{m! (n - 2)!} 	imes \frac{m! n!}{(m + n)!}$$P = \frac{n(n - 1)}{(m + n)(m + n - 1)}$.

$A$. Probability that none of the balls is white	$I$. $\frac{1}{70}$
$B$. Probability of getting $2$ white and $1$ blue ball	$II$. $\frac{6}{35}$
$C$. Probability of getting $2$ blue and $1$ white ball	$III$. $\frac{13}{20}$
$D$. Probability of getting $1$ red, $1$ white and $1$ blue ball	$IV$. $\frac{1}{10}$

If $m$ rupee coins and $n$ ten paise coins are placed in a line,then the probability that the extreme coins are ten paise coins is

Similar Questions

Let $S$ be the set of all the words that can be formed by arranging all the letters of the word $\text{GARDEN}$. From the set $S$,one word is selected at random. The probability that the selected word will $\text{NOT}$ have vowels in alphabetical order is:

If five-digit numbers are formed from the digits $0, 1, 2, 3, 4$ using every digit exactly once,then the probability that a randomly chosen number from those numbers is divisible by $4$ is:

$A$ bag contains $4$ white and $3$ red balls. Two draws of one ball each are made without replacement. Then the probability that both the balls are red is

In a certain lottery,$10,000$ tickets are sold and $10$ equal prizes are awarded. What is the probability of not getting a prize if you buy $10$ tickets?

Vedclass Test Series

Exam Paper Generator

Online Exam Module