Statistics And Probability Question 293
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}} $
Show Answer
Answer:
Correct Answer: B
Solution:
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As we know the total number of mappings is $ n^{m} $ and number of injective mappings is $ \frac{n!}{(n-m)\,!n^{m}} $ .
BETA
