Question
Question: If A = {1, 2, 3}, B = {1, 2, 3, 4, 5}. the no. of functions from A to B such that f(i)≤f(j) when i i...
If A = {1, 2, 3}, B = {1, 2, 3, 4, 5}. the no. of functions from A to B such that f(i)≤f(j) when i is
A
125
B
25
C
35
D
50
Answer
35
Explanation
Solution
f: A → B such that f(i) ≤ f(j) when ever i ≤ j.
f(1) - No. of ways of selecting and arranging 3 elements
= 5C3.1
f(2) - No. of ways of selecting and arranging 2 elements
= 2.5C2
f(3) - No. of ways of selecting and arranging 1 element = 5C1.
Total no. of ways = 5C3+2.5C2+5C1.