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# Private Benjamin is a member of a squad of 10 soldiers, which must vol

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Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

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13 Jul 2015, 12:14
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Question Stats:

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Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5
[Reveal] Spoiler: OA

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Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

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13 Jul 2015, 12:19
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reto wrote:
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5

Direct approach:

$$\frac{C^1_1*C^3_9}{C^4_{10}}=\frac{2}{5}$$.

Reverse approach:

1 - (the probability of 4-member groups without Benjamin) = $$1 -\frac{C^4_9}{C^4_{10}}=\frac{2}{5}$$.

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Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

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13 Jul 2015, 12:30
reto wrote:
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5

Easier way : Desired probability = 1- 'excluded' probability

In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.

Thus excluded probability = 9C4/10C4 = 3/5

Thus, the desired probability = 1- 3/5 = 2/5. Thus C is the correct answer.

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Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

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13 Jul 2015, 12:37
Bunuel wrote:
reto wrote:
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5

Direct approach:

$$\frac{C^1_1*C^3_9}{C^4_{10}}=\frac{2}{5}$$.

Reverse approach:

1 - (the probability of 4-member groups without Benjamin) = $$1 -\frac{C^4_9}{C^4_{10}}=\frac{2}{5}$$.

Is there a simple way to reduce $$\frac{C^1_1*C^3_9}{C^4_{10}}$$ to 2/5 or do you also have to split it up to 9*8*7/3*2*1 / 210 and then go from there...?
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Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

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13 Jul 2015, 12:45
1
KUDOS
reto wrote:
Bunuel wrote:
reto wrote:
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5

Direct approach:

$$\frac{C^1_1*C^3_9}{C^4_{10}}=\frac{2}{5}$$.

Reverse approach:

1 - (the probability of 4-member groups without Benjamin) = $$1 -\frac{C^4_9}{C^4_{10}}=\frac{2}{5}$$.

Is there a simple way to reduce $$\frac{C^1_1*C^3_9}{C^4_{10}}$$ to 2/5 or do you also have to split it up to 9*8*7/3*2*1 / 210 and then go from there...?

you can look it at like this:

Remove Benjamin from the equation for now. You have 10 people from which only 9 are applicable to choose 4 volunteers from.

Thus the probabilities of selecting 1st,2nd , 3rd and 4th volunteers will be : (9/10) [you have 9 favorable choices out of 10 available], (8/9)[you have 8 favorable choices out of 9 available], (7/8)[you have 7 favorable choices out of 8 available], (6/7)[you have 6 favorable choices out of 17 available] .

The final probability (without Benjamin) will be (9/10)*(8/9)*(7/8)*(6/7) = 3/5.

Thus the Probability with Benjamin selected = 1-3/5 = 2/5.

As far as reducing nCr is concerned, there is only 1 formula: nCr = n!/ [r!*(n-r)!)]

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Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

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01 Jun 2016, 12:00
If we assume that Benjamin is volunteering to be on the 4 group can we derive 4/10 =2/5 no??
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Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

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09 Oct 2017, 09:21
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Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

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12 Oct 2017, 18:03
reto wrote:
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5

The number of ways 4 people can be chosen from 10 is 10C4 = 10!/[4!(10-4)!] = (10 x 9 x 8 x 7)/(4 x 3 x 2 x 1) = 10 x 3 x 7.

If Private Benjamin must be 1 of the 4 people chosen, then we have to choose 3 people from the remaining 9 people. The number of ways 3 people can be chosen from 9 is 9C3 = 9!/[3!(9-3)!] = (9 x 8 x 7)/(3 x 2 x 1) = 3 x 4 x 7.

Thus, the probability that Private Benjamin will be chosen for latrine duty is:

9C3/10C4 = (3 x 4 x 7)/(10 x 3 x 7) = 4/10 = 2/5

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Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol   [#permalink] 12 Oct 2017, 18:03
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