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If 2n boys are divided into two equal subgroups find the probability that the two tallest boys will be in different subgroups and in the same subgroup.

Question

If 2n boys are divided into two equal subgroups find the probability that the two tallest boys will be in different subgroups and in the same subgroup.

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Step 1

No of ways to divide 2n boys into two subgroup is 

(2n!)
=>
2 x n! x n!
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(2n!) => 2 x n! x n!

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Step 2

Let the two tallest be in one group , so favourable no of ways of choosing

(2п-2)!
=2n-2Cn-2 (n-2)!n!
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(2п-2)! =2n-2Cn-2 (n-2)!n!

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Step 3

So the probability that the two tall...

favourable no of choosing
=>
Total no of ways
(2n 2)!
(п - 2)! n!
(2n!)
2 x n! X n!
(2п — 2)! x п! х (п — 1) x (п — 2)! x 2
n-1
2n 1
(п - 2)! x п! x (2n) x (2n — 1) х (2n — 2)!
_
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favourable no of choosing => Total no of ways (2n 2)! (п - 2)! n! (2n!) 2 x n! X n! (2п — 2)! x п! х (п — 1) x (п — 2)! x 2 n-1 2n 1 (п - 2)! x п! x (2n) x (2n — 1) х (2n — 2)! _

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