A bag contains n white and n black balls. Pai | vedclass

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

Question

(B) The total number of ways to draw $n$ pairs of balls such that each pair contains one white and one black ball is given by the product of the numbe

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) The total number of ways to draw $n$ pairs of balls such that each pair contains one white and one black ball is given by the product of the number of ways to choose one white and one black ball for each successive draw.For the first draw,there are $n$ white and $n$ black balls. The number of ways to pick one white and one black ball is $\binom{n}{1} 	imes \binom{n}{1} = n^2$.For the second draw,there are $(n-1)$ white and $(n-1)$ black balls remaining. The number of ways is $\binom{n-1}{1} 	imes \binom{n-1}{1} = (n-1)^2$.Continuing this until the last pair,the total number of ways is $(n 	imes (n-1) 	imes \dots 	imes 1)^2 = (n!)^2$.Given that $(n!)^2 = 14400$,we have $n! = \sqrt{14400} = 120$.Since $5! = 120$,we find $n = 5$.

$A$ bag contains $n$ white and $n$ black balls. Pairs of balls are drawn at random without replacement successively,until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is $14400$,then $n$ is equal to

Similar Questions

The number of all possible positive integral solutions of the equation $xyz=30$ is

Four-digit numbers are formed using the digits $1, 2, 3, 4$ (repetition is allowed). The number of such four-digit numbers divisible by $11$ is

The number of positive integral solutions of $abc = 30$ is

Five balls of different colours are to be placed in three boxes of different sizes. The number of ways in which we can place the balls in the boxes so that no box remains empty is

Among the inequalities below,which ones are true for all natural numbers $n > 1000$?
$I. n! \leq n^n$
$II. (n!)^2 \leq n^n$
$III. 10^n \leq n!$
$IV. n^n \leq (2n)!$

Vedclass Test Series

Exam Paper Generator

Online Exam Module