Many Injections

Probability Level 2

For two sets X = { a , b , c } , Y = { y ∣ 1 ≤ y ≤ 6 , y is an integer } , X=\{a,b,c\}, Y=\{y\mid 1 \leq y \leq 6, y \text{ is an integer}\}, how many injective functions f : X → Y f: X \to Y exist?

240 360 120 720

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Mahindra Jain by Mahindra Jain

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1 solution

Raj Magesh
May 4, 2014

An injective function (or a one-to-one function) relates each element in set X to an element in set Y such that no two elements in X relate to the same element in Y. This means that each arrow points to a different element of Y, from 1 to 6. Since there are 3 elements in X that have to be assigned to any 3 elements out of 6 elements in Y, there are a total of 6 P 4 = 120 ^{6}P_4 = \boxed{120} possible ways to do it.

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