Probability Question 428
Question: Let A and B be two finite sets having m and n elements respectively such that $ m\le n., $ A mapping is selected at random from the set of all mappings from A to B. The probability that the mapping selected is an injection is
Options:
A) $ \frac{n,!}{(n-m),!,m^{n}} $
B) $ \frac{n,!}{(n-m),!,n^{m}} $
C) $ \frac{m,!}{(n-m),!,n^{m}} $
D) $ \frac{m,!}{(n-m),!,m^{n}} $
Correct Answer: B
Show Answer
Answer:
Solution:
As we know the total number of mappings is $ n^{m} $ and number of injective mappings is $ \frac{n!}{(n-m)\,!n^{m}} $ .
BETA
