First slide

Permutations

Question

If m = number of distinct rational numbers $\frac{p}{q} \in (0, 1)$ such that p, q ∈ {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

None of these

Solution

Now, n = 2³ – 2 = 6
Also, $m = 4 + 3 + 2 + 1 - 1 = 9 (as \frac{2}{4} = \frac{1}{2})$
∴ m – n = 3

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