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# What is the probability of choosing 2 distinct positive integers from

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Director
Joined: 18 Feb 2019
Posts: 582
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
What is the probability of choosing 2 distinct positive integers from  [#permalink]

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14 Apr 2019, 07:41
1
1
00:00

Difficulty:

45% (medium)

Question Stats:

54% (01:33) correct 46% (01:08) wrong based on 24 sessions

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What is the probability of choosing 2 distinct positive integers from the set of first 10 positive integers such that their product and sum are both even?

A. 1/5
B. 2/9
C. 2/5
D. 4/9
E. 1/2
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1021
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: What is the probability of choosing 2 distinct positive integers from  [#permalink]

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14 Apr 2019, 10:28
First 10 positive integers = {1,2,3,4,5,6,7,8,9,10}
Ways to choose 2 positive integers = $$10C_2$$ = 45.
Only group of even numbers can give sum and product to be even.
Possible groups are, (2,4) (2,6) (2,8) (2,10) (4,6) (4,8) (4,10) (6,8) (6,10) (8,10) = 10 groups.

Probability = 10/45 = 2/9

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Re: What is the probability of choosing 2 distinct positive integers from   [#permalink] 14 Apr 2019, 10:28
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