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Lottery game with great odds!

Expert replies
by XLogic » Sat Apr 14, 2012 10:06 am
To win a particular lottery game, a player chooses 4 numbers from 1 to 10. Each number can only be chosen once. If all 4 numbers match the 4 winning numbers, regardless of order, the player wins. What is the likelihood that the winning numbers are 3, 2, 7, and 5.

A) 1/5040
B) 1/10000
C) 1/21
D) 1/210
E) 1/10

(source: revised from khanacademy.org)
[spoiler]https://www.khanacademy.org/math/probabi ... inations-4[/spoiler]
Last edited by XLogic on Sat Apr 14, 2012 10:20 am, edited 1 time in total.
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Source: — Problem Solving |

by Shalabh's Quants » Sat Apr 14, 2012 10:17 am
XLogic wrote:To win a particular lottery game, a player chooses 4 numbers from 1 to 10. Each number can only be chosen once. If all 4 numbers match the 4 winning numbers, regardless of order, the player wins. What is the likelihood that the winning numbers are 3, 2, 7, and 5.

(source: revised from khanacademy.org)

A) 1/5040
B) 1/10000
C) 1/21
D) 1/210
E) 1/10
=> p(winning) = Ways of choosing particular 4 nos./Tot. nos. of ways of choosing 4 nos. out of 10 nos.

=> = 4C4/10C4 = 1/210. Ans D.
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by XLogic » Sat Apr 14, 2012 10:23 am
@Shalabh, if you were to rate this problem in terms of GMAT difficulty, where would you put it?
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by Shalabh's Quants » Sat Apr 14, 2012 11:00 am
XLogic wrote:@Shalabh, if you were to rate this problem in terms of GMAT difficulty, where would you put it?
Medium level
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by seal4913 » Sat Apr 14, 2012 1:44 pm
XLogic wrote:To win a particular lottery game, a player chooses 4 numbers from 1 to 10. Each number can only be chosen once. If all 4 numbers match the 4 winning numbers, regardless of order, the player wins. What is the likelihood that the winning numbers are 3, 2, 7, and 5.

A) 1/5040
B) 1/10000
C) 1/21
D) 1/210
E) 1/10

(source: revised from khanacademy.org)
[spoiler]https://www.khanacademy.org/math/probabi ... inations-4[/spoiler]
Another way to look at it is, the first pick can be any of the 4 winning nubmers so 4/10, then 3/9, 2/8, and 1/7

2/5 * 1/3 * 1/4 * 1/7 = 2/420 = 1/210 which is D
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