# Set Theory, Calendars, Clocks and Binomial Theorem

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## Set Theory and Combinatorics

Set A = {2, 3, 5, 6, 7}, Set B = {a, b, c}. How many onto functions can be defined from Set B to Set A?
1. 2
2. 3
3. 4
4. None of the above

Choice D. None of the above

## Detailed Solution

Number of onto function from Set A to Set B:
There are 3 elements in set B, all these elements need to be mapped to some element in set A.
For a function to exist every element of the domain has a unique value.
a of Set B can be mapped to any of the 5 elements of Set A
b of Set B can be mapped to any of the other 4 elements in Set A and
c of Set B can be mapped to any of the other 3 elements in Set A
Thus the number of onto functions that can be obtained is 5*4*3=60

Number of onto function from Set B to Set A:
There are 5 elements in Set A whereas there are only 3 elements in Set B, which effectively means only 3 elements of Set A at the max can be mapped to Set B.
For a function to exist every element of the domain has a unique value.
Thus no onto function can be defined from set B to Set A

Correct Answer: None of the above.

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