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:

Probability of a one–one mapping on an n-set is (n!)/(nⁿ).

Answer 1

The Correct Option is B

Step 1: Total mappings from a set of n elements into itself: nⁿ Step 2: Number of one–one mappings (permutations): n! Step 3: Given probability: (n!)/(nⁿ)=(3)/(32) Step 4: Checking values: n=4 ⟹ (4!)/(4⁴)=(24)/(256)=(3)/(32) Hence, n=4.