The number of ways of forming the ordered pai | vedclass

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Question

(C) To form an ordered pair $(p, q)$ such that $p > q$ from the set $S = \{1, 2, 3, \dots, 50\}$,we need to choose $2$ distinct numbers from the $50$

Vedclass · Accepted Answer

$1225$

Vedclass · Answer

(C) To form an ordered pair $(p, q)$ such that $p > q$ from the set $S = \{1, 2, 3, \dots, 50\}$,we need to choose $2$ distinct numbers from the $50$ available numbers.Let the chosen numbers be $x$ and $y$ where $x For any such pair,there is exactly one way to assign them to $p$ and $q$ such that $p > q$,which is $p = y$ and $q = x$.The number of ways to choose $2$ distinct numbers from $50$ is given by the combination formula $\binom{n}{r}$.Here,$n = 50$ and $r = 2$.Number of ways = $\binom{50}{2} = \frac{50 	imes 49}{2 	imes 1} = 25 	imes 49 = 1225$.

The number of ways of forming the ordered pairs $(p, q)$ such that $p > q$ by choosing $p$ and $q$ from the first $50$ natural numbers is

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