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# If three integers from among the first 10 positive integers are chosen

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BSchool Forum Moderator
Joined: 26 Feb 2016
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If three integers from among the first 10 positive integers are chosen [#permalink]

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07 Mar 2018, 09:26
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72% (01:40) correct 28% (01:00) wrong based on 25 sessions

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If three integers from among the first 10 positive integers are chosen, what is the probability that the product of these integers is even?

A. $$\frac{1}{12}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{6}$$
D. $$\frac{3}{4}$$
E. $$\frac{11}{12}$$

Source: Experts Global
[Reveal] Spoiler: OA

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Re: If three integers from among the first 10 positive integers are chosen [#permalink]

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08 Mar 2018, 03:26
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pushpitkc wrote:
If three integers from among the first 10 positive integers are chosen, what is the probability that the product of these integers is even?

A. $$\frac{1}{12}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{6}$$
D. $$\frac{3}{4}$$
E. $$\frac{11}{12}$$

Source: Experts Global

Best way would be to find when it is not EVEN...
Choose odd =5C3
Choose any three = 10C3
Prob = $$\frac{5C3}{10C3}=\frac{5*4*3}{10*9*8}=\frac{1}{12}$$
So prob of even=1- 1/12=11/12
E
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Joined: 09 Jun 2016
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Re: If three integers from among the first 10 positive integers are chosen [#permalink]

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08 Mar 2018, 14:02
Hi can one solve considering every 6 nos. As I am getting 1/6 as answer

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Re: If three integers from among the first 10 positive integers are chosen [#permalink]

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12 Mar 2018, 10:10
pushpitkc wrote:
If three integers from among the first 10 positive integers are chosen, what is the probability that the product of these integers is even?

A. $$\frac{1}{12}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{6}$$
D. $$\frac{3}{4}$$
E. $$\frac{11}{12}$$

We can use the formula:

P(even product) = 1 - (probability of an odd product)

In order to get an odd product we need 3 odd integers. The probability of selecting 3 odd integers is:

5/10 x 4/9 x 3/8 = 1/2 x 1/3 x 1/2 = 1/12

So the probability of an even product is 1 - 1/12 = 11/12.

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Re: If three integers from among the first 10 positive integers are chosen   [#permalink] 12 Mar 2018, 10:10
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