First slide

Permutations

Question

If x < 4 < y $x, y \in {1, 2, 3, \dots, 10}$ then find the number of ordered pairs (x, y)

Moderate

A

30
B

18
C

40
D

100

Solution

We have, x< 4 < y
where, $x, y \in {1, 2, 3, \dots, 10}$
$\Rightarrow x = {1, 2, 3} and y = {5, 6, 7, 8, 9, 10}$
x = {1, 2, 3} and y ={5, 6, 7, B, 9, 10}
Here, x have 3 options and y have 6 options
By multiplication rule,
Number of ordered pairs=3x6=18

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