Question

One mapping is selected at random from all mappings of the set S=1,2,3,… ,n into itself. The probability that it is one–one is (3)/(32). Then the value of n is

• A. 3
• B. 4
• C. 5
• D. 6

Hint:

One–one mappings from a set to itself equal permutations.

Answer 1

The Correct Option is B

Step 1: Total mappings =nⁿ.
Step 2: One–one mappings =n!. (n!)/(nⁿ)=(3)/(32)
Step 3: Checking options, for n=4: (4!)/(4⁴)=(24)/(256)=(3)/(32).