Question

Consider the set of all functions from {1, 2, . . . ,m} to {1, 2, . . . , n}, where n > m. If a function is chosen from this set at random, the probability that it will be strictly increasing is

Answer 1

From A to B number of functions = n^m

Number of increasing (strictly)

functions = ⁿCm

[Becuase , out of m integers

there is only one arrangement in which integers are in ascending order ]

Therefore,

Probability = ⁿCm/n^m

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