How many differents pairs(m, n)can be formed using numbers from the list of whole numbers {1,2,3,320} such that m

Complete question :

How many different pairs (m, n) can be formed using numbers from the list of whole numbers { 1, 2, 3, ..., 20 } such that m < n and m + n is even?

90

Step-by-step explanation:

Given :

Condition :

m < n ; m + n = even number

Thus ;

m = 1 ; n = 3, 5, 7, 9, 11, 13, 15, 17, 19 = 9

m = 2; n = 4, 6, 8, 10, 12, 14, 16, 18, 20 = 9

m = 3 ; n = 5, 7, 9, 11, 13, 15, 17, 19 = 8

m = 4 ; n = 6, 8, 10, 12, 14, 16, 18, 20 = 8

m = 5 ; n = 7, 9, 11, 13, 15, 17, 19 = 7

m = 6 ; n = 8, 10, 12, 14, 16, 18, 20 = 7

Observing the trend :

For ;

m = 7, number of ways = 6

m = 8, number of ways = 6

m = 9, number of ways = 5

m = 10, number of ways = 5

m = 11, number of ways = 4

m = 12, number of ways = 4

m = 13, number of ways = 3

m = 14, number of ways = 3

m = 15, number of ways = 2

m = 16, number of ways = 2

m = 17, number of ways = 1

m = 18, number of ways = 1

m = 19, Number of ways = 0

Hence,

(9+9+8+8+7+7+6+6+5+5+4+4+3+3+2+2+1+1) =90

Hence, we have 90 (m, n) pairs