counting techniques

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iamnikkilarin: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Wed Aug 15, 2012 4:29 am

by iamnikkilarin » Wed Aug 15, 2012 4:41 am

A sales representative for a company must visit 6 different cities
exactly one time each. In how many different orders can the
cities be visited?

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Source: Beat The GMAT — Problem Solving | Wed Aug 15, 2012 4:41 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Aug 15, 2012 6:14 am

iamnikkilarin wrote:A sales representative for a company must visit 6 different cities
exactly one time each. In how many different orders can the
cities be visited?

Here we want to arrange 6 unique items (cities) in a row.

In general, we can arrange n unique objects in n! ways.

So, the total number of ways to arrange 6 cities is 6!, which equals [spoiler]6x5x4x3x2x1 = 720[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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