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# Two numbers, X and Y, are to be chosen at random from the set of numbe

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Math Expert
Joined: 02 Sep 2009
Posts: 60555
Two numbers, X and Y, are to be chosen at random from the set of numbe  [#permalink]

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07 Apr 2016, 08:35
00:00

Difficulty:

45% (medium)

Question Stats:

75% (02:26) correct 25% (02:42) wrong based on 67 sessions

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Two numbers, X and Y, are to be chosen at random from the set of numbers A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. If it is assumed that {X = a, Y = b} is the same as the event {X = b, Y = a} for any numbers a and b in A, what is the probability that X^2 + Y^2 ≤ 27?

A. 13/90
B. 7/45
C. 17/90
D. 11/45
E. 23/90

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Joined: 28 Feb 2014
Posts: 289
Location: United States
Concentration: Strategy, General Management
Re: Two numbers, X and Y, are to be chosen at random from the set of numbe  [#permalink]

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07 Apr 2016, 17:11
Two numbers, X and Y, are to be chosen at random from the set of numbers A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. If it is assumed that {X = a, Y = b} is the same as the event {X = b, Y = a} for any numbers a and b in A, what is the probability that X^2 + Y^2 ≤ 27?

X^2 + Y^2 has to be ≤ 27

10! / 2!8!
there are 45 possible combinations in total

only pairs that result in a value of ≤ 27 include:
5,1
4,3
4,2
4,1
3,2
3,1
2,1

B. 7/45
Re: Two numbers, X and Y, are to be chosen at random from the set of numbe   [#permalink] 07 Apr 2016, 17:11
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