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?
Answers
Given : 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
To Find : How many different pairs
Solution:
m = 1 n Can be 3 , 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 = 9 Pairs
m = 2 n can be 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 = 9 Pairs
m = 3 n can be 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 = 8 Pairs
m = 4 n can be 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 = 8 Pairs
m = 17 n can be 19 - 1 pair
m = 18 n can be 20 1 pair
So total pairs
= 9 + 9 + 8 + 8 + 7 + 7 + ......................................+ 1 + 1
= 2 ( 9 + 8 + 7 + ..............+ 1)
= 2 ( 9 (10) /2
= 90
90 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
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