Complicated Math Question...
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Complicated Math Question...

[From: ] [author: ] [Date: 12-01-26] [Hit: ]
Let 2 (2!) be the number needed to divide the odds since the order of how they are chosen wont matter.If you cancel out the fractions, the answer becomes 1/87296.......
Two integers are selected from the first 1024 positive integral perfect squares. What is tthe probability that both of these numbers are fifth powers of integers?

Options: 1/ 256, 1/ 174592, 3/ 1024, 1/ 43648, 1/ 87296

And please explain if you could just to make it clear for me.

Thx

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Not sure I under stand the question correctly but:
1024 x 1024 = 1048576
So your set of perfect numbers would be
(1,4,9,16,....1048576)

What is the highest fifth power under 1048576?
What is the 5th root of 1048576?
Answer is 16
16^5 = 1048576

Since there are 1024 perfect numbers and only the first 4 numbers in the set would be 5th roots under 1048576 I believe you set up the equation for combination for probablilty

Let 4/1024 be the odds that the first integer chosen would be a 5th root.
Let 3/1023 be the odds of the second integer chosen that would be a fifth root.
Let 2 (2!) be the number needed to divide the odds since the order of how they are chosen won't matter.

(4/1024) x (3/1023) / (2)

If you cancel out the fractions, the answer becomes 1/87296.
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