First slide

Permutations

Question

If m = number of distinct rational numbers $\frac{p}{q} \in (0, 1)$ such that $p, q \in {1, 2, 3, 4, 5}$ and n = number of mappings from {1, 2, 3} onto {1, 2}, then m – n is

Moderate

A

1
B

-1
C

0
D

3

Solution

Now, $n = 2^{3} - 2 = 6$
Also, $m = 4 + 3 + 2 + 1 - 1 = 9 (as \frac{2}{4} = \frac{1}{2})$
$∴ m - n = 3$

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