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This is how Edward’s Lotteries work. First, 9 different numb

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This is how Edward’s Lotteries work. First, 9 different numb [#permalink]

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New post 21 Mar 2010, 20:54
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This is how Edward’s Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottery system. How many tickets can the lottery system print?

(A) 9P6
(B) 9P3
(C) 9C9
(D) 9C6
(E) 69
[Reveal] Spoiler: OA
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Re: Permutation and Combination question [#permalink]

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New post 21 Mar 2010, 22:05
mads wrote:
This is how Edward's Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottory system. How many tickets can the lottery system print?
A. 9P6
B. 9P3
C. 9C9
D. 9C6
E. 6^9

OA after some discussion.

since we have to select random 6 numbers from 9 and they all are distinct. i think it should be 9C6 or D.
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Re: Permutation and Combination question [#permalink]

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New post 22 Mar 2010, 08:05
mads wrote:
This is how Edward's Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottory system. How many tickets can the lottery system print?
A. 9P6
B. 9P3
C. 9C9
D. 9C6
E. 6^9

OA after some discussion.


Here order does matter hence we need to choose permutation = 9P6.
Suppose numbers are 1,2,3,4,5,6 so
123456 is not same as 654321 hence order matters
hence A.
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Re: Permutation and Combination question [#permalink]

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New post 22 Mar 2010, 08:10
sidhu4u wrote:
mads wrote:
This is how Edward's Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottory system. How many tickets can the lottery system print?
A. 9P6
B. 9P3
C. 9C9
D. 9C6
E. 6^9

OA after some discussion.

since we have to select random 6 numbers from 9 and they all are distinct. i think it should be 9C6 or D.

Question wants to know how many ways six randomly selected numbers can be printed hence we need to use permutation instead of combination. As 123456 is not same as 654321.
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Re: Permutation and Combination question [#permalink]

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New post 22 Mar 2010, 11:10
mads wrote:
This is how Edward's Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottory system. How many tickets can the lottery system print?


I chose 9C6 because of the highlighted sections above. It is not mentioned that the order matters, just that no two tickets have the same set of numbers.
If order mattered then 9P6 would be correct.

What is the OA?
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Re: Permutation and Combination question [#permalink]

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New post 22 Mar 2010, 20:19
sidhu4u wrote:
mads wrote:
This is how Edward's Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottory system. How many tickets can the lottery system print?


I chose 9C6 because of the highlighted sections above. It is not mentioned that the order matters, just that no two tickets have the same set of numbers.
If order mattered then 9P6 would be correct.

What is the OA?

But the question is asking what is highlighted above.
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Re: Permutation and Combination question [#permalink]

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New post 22 Mar 2010, 22:44
mads wrote:
This is how Edward's Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottory system. How many tickets can the lottery system print?
A. 9P6
B. 9P3
C. 9C9
D. 9C6
E. 6^9

OA after some discussion.



Well friends it is clearly mentioned that no tickets have the same set of numbers and how many tickets can the lottery system print. Here we go with combination

IMO 9C6

Ex- How many times can a party of six students be arranged out of 9 students so that no two parties are idenical

Here, we have to select 6 out of 9. Therefore, the total no. of parties 9C6

What is OA?
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This is how Edward’s Lotteries work. First, 9 different numb [#permalink]

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New post 28 Jun 2017, 08:37
mads wrote:
This is how Edward’s Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottery system. How many tickets can the lottery system print?

(A) 9P6
(B) 9P3
(C) 9C9
(D) 9C6
(E) 69

We need to arrange the 6 selected numbers to form different ticket# as well. For instance, if 012345 get selected, then we can arrange this digits to form various numbers, such as 321450 or 123045 or 513042 etc. Hence, order does matter so answer should be A 9P6.
The OA needs to be corrected.

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Re: This is how Edward’s Lotteries work. First, 9 different numb [#permalink]

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New post 31 Jan 2018, 04:00
Bunuel
can u please help with this question?
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Re: This is how Edward’s Lotteries work. First, 9 different numb [#permalink]

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New post 31 Jan 2018, 05:35
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Re: This is how Edward’s Lotteries work. First, 9 different numb [#permalink]

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New post 31 Jan 2018, 08:42
mads wrote:
This is how Edward’s Lotteries work. First, 9 different numbers are selected. Tickets with exactly 6 of the 9 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 9 randomly. There is exactly one winning ticket in the lottery system. How many tickets can the lottery system print?

(A) 9P6
(B) 9P3
(C) 9C9
(D) 9C6
(E) 69


6 of the 9 numbers are selected first. (Usually the numbers on lottery tickets are 1 or 2 digit)
There are no two tickets with the same set of numbers i.e. no two tickets will have the same 6 numbers. Note that there is no mention of arrangement of the numbers. Just that all 6 numbers should not match. They could be arranged in any way while being printed such as

12, 6, 84, 19, 2, 91

OR

12, 6, 84
19, 2, 91

OR

12, 6
84, 91
2, 19

and so on...

So we will be able to make unique lottery tickets using 9C6.

Answer (D)
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Re: This is how Edward’s Lotteries work. First, 9 different numb   [#permalink] 31 Jan 2018, 08:42
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