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# What is the probability that exactly two of the six numbers appear on

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Senior Manager
Joined: 12 Jan 2019
Posts: 263
What is the probability that exactly two of the six numbers appear on  [#permalink]

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12 Jan 2019, 08:56
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Difficulty:

65% (hard)

Question Stats:

40% (02:22) correct 60% (01:38) wrong based on 10 sessions

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What is the probability that exactly two of the six numbers appear on the top face in the six throws of an unbiased die?

a. $$\frac{1}{729}$$

b. $$\frac{15}{729}$$

c. $$\frac{155}{6^5}$$

d. $$\frac{13}{729}$$

e. $$\frac{2}{243}$$

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Senior Manager
Joined: 12 Jan 2019
Posts: 263
Re: What is the probability that exactly two of the six numbers appear on  [#permalink]

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12 Jan 2019, 09:01
$$\frac{(6C2x(2^6-2))}{6^6}$$
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Concentration: Operations, Finance
GMAT 1: 650 Q48 V31
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Re: What is the probability that exactly two of the six numbers appear on  [#permalink]

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12 Jan 2019, 10:33
What is the probability that exactly two of the six numbers appear on the top face in the six throws of an unbiased dice?

Ans: total ways = 6^6
Selecting any 2 number : 6c2
Lets say two numbers selected be : a and b out of 6, then in 6 rolls:
Case 1: a,a,a,a,a,b or b,b,b,b,b,a
No of Ways- 2*6!/5!

Case 2: a,a,a,a,b,b or b,b,b,b,a,a
No of Ways- 2*6!/4!*2!

Case 3: a,a,a,b,b,b
No of Ways- 6!/3!*3!

Totalling we get : 62

Ans : 6c2*62/6^6 = 155/6^5

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Re: What is the probability that exactly two of the six numbers appear on   [#permalink] 12 Jan 2019, 10:33
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