probablity qn

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kishokbabu: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed May 04, 2011 9:50 pmFollowed by: 2 members; Thanked: 2 times

by kishokbabu » Tue Dec 13, 2011 11:12 am

John and Bill are among 5 runners in a race where there are no ties. How many ways is it possible for john to finish the race ahead of Bill?

A) 5
B) 10
C) 30
D) 60
E) 120

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Source: Beat The GMAT — Problem Solving | Tue Dec 13, 2011 11:12 am

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Tue Dec 13, 2011 11:22 am

kishokbabu wrote:John and Bill are among 5 runners in a race where there are no ties. How many ways is it possible for john to finish the race ahead of Bill?

A) 5
B) 10
C) 30
D) 60
E) 120

There are 5! (120) number of ways a race with 5 runners could end

There are two kinds of cases
Either John finishes after Bill or John finishes b4 Bill

The number of way John finishes ahead of Bill is exactly half of total possibilities => 120/2 => 60

Option D

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Mdewan: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Dec 04, 2011 10:02 pm; Thanked: 2 times

by Mdewan » Tue Dec 13, 2011 2:00 pm

Option C

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kdas: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Dec 13, 2011 4:19 pm; Thanked: 3 times

by kdas » Tue Dec 13, 2011 4:26 pm

60 ways

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MakeUrTimeCount: Master | Next Rank: 500 Posts; Posts: 104; Joined: Sun Dec 11, 2011 1:25 pmFollowed by: 3 members; Thanked: 11 times

by MakeUrTimeCount » Wed Dec 14, 2011 3:20 am

If John comes 1st, then Bill should be among 2 to 5 position, so ways = 4
If John comes 2nd, then Bill should be among 3 to 5 position, so ways = 3
If John comes 3rd, then Bill should be among 4 to 5 position, so ways = 2
If John comes 4th, then Bill should be 5th, so ways = 1

Total = 4 + 3+ 2+ 1 = 10
At the same time, other 3 racer's positions can be adjusted in 3! ways.

So 3! . 10 = 60
Option: D

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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Wed Dec 14, 2011 12:05 pm

or vice verse-
if B is the last one, then J has 4 options
if B is in the 4th place, then J has 3 options
if B is in the 3rd place, then J has 2 options
if B is in the 2nd place, then J has only 1 option
so, (4+3+2+1)*3!=60 (3!-the way to arrange the rest 3 ppl)

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