Q. 325.0( 1 Vote )

# One mapping is selected at random from all the mappings of the set A = {1, 2, 3, ….., n) into itself. The probability that the mapping selected is one to one is

A.

B.

C.

D. none of these

Answer :

We know that the no of mapping from a set A to same set containing n elements = n^{n}

As each element have n options to be mapped with n elements.

For mapping selected to be one to one, for first element we have n options ,for second we have n-1 options an so on…

∴ total such mappings = n × (n-1)× (n-2)× … = n!

∴ P(mapping is one to one) =

Our answer matches with option (c)

∴ Option (c) is the only correct choice

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