GATE | GATE CS 1997 | Question 57

Let F be the set of one-to-one functions from the set {1,2,…,n} to the set {1,2,…,m}, where m ≥n ≥ 1.

a. How many functions are members of F?
b. How many functions f in F satisfy the property f(i)=1 for some i, 1 ≤ i ≤ n?
c. How many functions f in F satisfy the property f(i) < f(j) for all 1 ≤ i ≤ j ≤ n?

Answer:

Explanation:

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