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
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.
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.