MathDB

Let

U=\{1, 2,\ldots, 2014\}

. For positive integers

a

b

c

we denote by

f(a, b, c)

the number of ordered 6-tuples of sets

(X_1,X_2,X_3,Y_1,Y_2,Y_3)

satisfying the following conditions: (i)

Y_1 \subseteq X_1 \subseteq U

and

|X_1|=a

; (ii)

Y_2 \subseteq X_2 \subseteq U\setminus Y_1

and

|X_2|=b

; (iii)

Y_3 \subseteq X_3 \subseteq U\setminus (Y_1\cup Y_2)

and

|X_3|=c

. Prove that

f(a,b,c)

does not change when

a

b

c

are rearranged.
Proposed by Damir A. Yeliussizov, Kazakhstan

Problem Statement