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

Question

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 (A) 6 (B) 5 (C) 4 (D) 3

Tardigrade Admin · Accepted Answer

According to the given condition ( n C1 n C1)( n-1 C1 n-1 C1) ldots( 1 C11 C1)=14400 ⇒ ( n Cn-1 C1 ldots 1 C1)2=(120)2 ⇒ n(n-1)(n-2) ldots 1=120 ⇒ n !=5 ! ⇒ n=5

Q. 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

6

5

4

3

According to the given condition
$(^{n} C_{1}^{n} C_{1}) (^{n - 1} C_{1}^{n - 1} C_{1}) \dots (^{1} C_{1}^{1} C_{1}) = 14400$
$\Rightarrow (^{n} C^{n - 1} C_{1} \dots^{1} C_{1})^{2} = (120)^{2}$
$\Rightarrow n (n - 1) (n - 2) \dots 1 = 120$
$\Rightarrow n! = 5!$
$\Rightarrow n = 5$

Q. 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

6

5

4

3

According to the given condition (nC1​nC1​)(n−1C1​n−1C1​)…(1C11​C1​)=14400 ⇒(nCn−1C1​…1C1​)2=(120)2 ⇒n(n−1)(n−2)…1=120 ⇒n!=5! ⇒n=5

Q. 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

According to the given condition
$(^{n} C_{1}^{n} C_{1}) (^{n - 1} C_{1}^{n - 1} C_{1}) \dots (^{1} C_{1}^{1} C_{1}) = 14400$
$\Rightarrow (^{n} C^{n - 1} C_{1} \dots^{1} C_{1})^{2} = (120)^{2}$
$\Rightarrow n (n - 1) (n - 2) \dots 1 = 120$
$\Rightarrow n! = 5!$
$\Rightarrow n = 5$