2

Part of 2022 Korea Junior Math Olympiad

Problems(1)

normal counting problem in KJMO 2022

Source: KJMO 2022 number 2

For positive integer

n

3

), find the number of ordered pairs

(a_1, a_2, ... , a_n)

of integers that satisfy the following two conditions
1. For positive integer

i

1

i

n

1

a_i

i

2. For positive integers

i,j,k

1

i

j

k

n

a_i = a_j

a_j

a_k

combinatoricscounting