Question 16

The total number of onto functions from {1,2,...10} to {1,2,.......9} is

Solution

The number of elements in set A = 10

The number of elements in set B = 9

for the mapping to be onto there will be a element in set B which has 2 pre-images from set A

Two elements can be selected in $$^{10}C_2 $$ ways and the elements in set B can be arranged in 9! ways

$$\therefore$$ No of onto functions = $$^{10}C_2 \times 9!$$

A is the correct answer

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