Combine like terms 9-5=9x-6x
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Answer:
The possible number of ways to select distinct (<em>a, b</em>) such that (<em>a </em>+<em> b</em>) is even is 534.
Step-by-step explanation:
The range 1 - 99 has 99 numbers, since 1 and 99 are inclusive.
Of these 50 numbers are odd and 49 are even.
The two distinct numbers <em>a </em>and <em>b</em> must have an even sum and <em>a</em> should be a multiple of 9.
The sum of two numbers is even only when both are odd or both are even.
The possible values that <em>a</em> can assume are,
<em>a</em> = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90 and 99}
Thus, <em>a</em> can assume 6 odd values and 5 even values.
- If <em>a</em> = odd number, then <em>b</em> can be any of the 49 out of 50 odd numbers.
Total number of ways to select <em>a</em> and <em>b</em> such that both are odd and their sum is even is:
<em />
- If <em>a</em> = even number, then <em>b</em> can be any of the 48 out of 50 even numbers.
Total number of ways to select <em>a</em> and <em>b</em> such that both are even and their sum is even is
<em />
Total number of ways to select distinct (<em>a, b</em>) such that (<em>a </em>+<em> b</em>) is even is =
Thus, the possible number of ways to select distinct (<em>a, b</em>) such that (<em>a </em>+<em> b</em>) is even is 534.