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Permutations and Combinations

If set A=r,s ...

Question

If set $A = {(r, s) | r, s \in W}$ , then the number of element(s) in set $A$ such that $^{5} C_{r} \cdot^{6} C_{s} = 1$ is

A

0

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B

2

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C

3

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D

4

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Solution

The correct option is D $4$
Given : $^{5} C_{r} \cdot^{6} C_{s} = 1$
We know, $^{n} C_{r} \in N$
$\Rightarrow$ Solution is possible only if $^{5} C_{r} =^{6} C_{s} = 1$
$\Rightarrow^{5} C_{r} = 1$ and $^{6} C_{s} = 1$
$\Rightarrow r = 0, 5$ and $s = 0, 6$

$∴$ Possible pairs $(0, 0), (0, 6), (5, 0), (5, 6)$
$\Rightarrow$ Number of elements in set $A = 4$

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Permutations and Combinations

Standard XIII Mathematics

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