Question

A is a set containing n₁ elements and B is another set containing n₂ elements. The number of non-decreasing functions from A → B is

(A)  n₁ + n₂ -1 C_n1

(B)   n₁ + n₂ - 1C_n2

(C)  ⁿ¹C_n2

(D)   ⁿ²C_n1

Answer 1

Correct option  (A)  n₁ + n₂ -1 C_n1

Number of functions (non-decreasing) is number of nonnegative integral solution of x₁ + x₂ + ...+ X_n2  = n₁ = ^{n₁ + n₂ -1}C_n1