MathDB

Higher Secondary P10

X

is a set of

n

elements.

P_m(X)

is the set of all

m

element subsets (i.e. subsets that contain exactly

m

elements) of

X

. Suppose

P_m(X)

has

k

elements. Prove that the elements of

P_m(X)

can be ordered in a sequence

A_1, A_2,...A_i,...A_k

such that it satisfies the two conditions: (A) each element of

P_m(X)

occurs exactly once in the sequence, (B) for any

i

such that

0<i<k

, the size of the set

A_i \cap A_{i+1}

m-1

Problem Statement