Question
Download Solution PDFHow many different pairs (x, y) can be formed using the numbers {1, 2, 3,..., 43) such that x < y and the sum of x and y is even?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Set of numbers = {1, 2, 3, ..., 43}
x + y is even
Formula used:
Total pairs where x < y = nC2 =
Even pairs condition: x + y is even ⇒ x and y both even or both odd
Calculation:
Total even numbers = 22
Total odd numbers = 21
Pairs from even numbers =
⇒ Pairs = 231
Pairs from odd numbers =
⇒ Pairs = 210
Total pairs = 231 + 210
⇒ Total = 441
∴ The correct answer is option (3).
Last updated on Dec 9, 2024
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