Math, asked by nicholashabib111, 5 months ago

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

Answered by amitnrw
4

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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