Injective Functions

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How many one-to-one functions can be defined from a set containing 4 distinct elements into a set containing 6 distinct elements, assuming standard function definitions apply?

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A one-to-one (injective) function assigns distinct images to distinct domain elements, so images must be chosen without repetition, a key idea linking functions to permutations in JEE Advanced. The first domain element has 6 possible images, the second has 5 remaining, the third 4, and the fourth 3, since each must avoid previously used codomain values. Multiplying gives 6×5×4×3 = 360 injective functions, which equals the permutation P(6,4). This sequential-choice argument is the standard archetype for counting injections. Option 1296 = 6^4 counts all functions allowing repetition, violating injectivity. Option 24 = 4! counts only bijections of a 4-set, ignoring the larger codomain. Option 1080 is an arithmetic distractor with no structural meaning. Therefore the number of injective functions is 360. Plausibility check: the count must be less than the total 6^4 = 1296 and greater than 4! = 24, and 360 comfortably lies between, confirming the permutation reasoning is dimensionally sensible.

Injective Functions

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