Odd numbers and arithmetic mean
Probability
Level
3
Find the arithmetic mean of all the odd numbers that can be formed using exactly 3 of the digits 8, 7, 6, 4 or 2.
The answer is 557.
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1 solution
The unit digit must be a 7 because the number is odd. You have 4 choices for the hundreds digit and 3 choices for the tens digit. 4x3=12 numbers.
Each of 8, 6, 4 and 2 will occur 3 times at the hundreds and tens position.
(8+6+4+2) x 3 x 100 + (8+6+4+2) x 3 x 10 + 12 x 7 x 1=6000 + 600 + 84 =6684
The mean is 6684/12 = 557