Combinatorics

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Abdulla: Master | Next Rank: 500 Posts; Posts: 328; Joined: Thu Aug 07, 2008 5:25 pm; Location: Philadelphia; Thanked: 4 times; GMAT Score:550

by Abdulla » Tue Dec 16, 2008 5:51 pm

An office manager must choose a five-digit lock code for the office door. The first and last digits of the code must be odd, and no repetition of digits is allowed. How many different lock codes are possible?

Can someone explain why 4 x 5 x 8 x 7 x 6 = 6,720
OR if there is another approach please share it.

Abdulla

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Source: Beat The GMAT — Problem Solving | Tue Dec 16, 2008 5:51 pm

brb588: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Mon Nov 17, 2008 11:35 pmFollowed by: 1 member; Thanked: 6 times

by brb588 » Tue Dec 16, 2008 6:22 pm

Hi.

Okay, five digits, two are odd, none can repeat. Let start with the first digit. From 0-9, there are five odd digits (1, 3, 5, 7, 9). The first digit has 5 options.

5 * _ * _ * _ * _

Now let's jump to the fifth digit. If no numbers repeat, there can only be four numbers that digit five can be:

5 * _ * _ * _ * 4

Now fill in the middle digits. Again, no numbers can repeat. Two digits are already filled in, leaving eight for the second digit, seven for the third digit, and six for the fourth.

5 * 8 * 7 * 6 * 4 = 6720

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Abdulla: Master | Next Rank: 500 Posts; Posts: 328; Joined: Thu Aug 07, 2008 5:25 pm; Location: Philadelphia; Thanked: 4 times; GMAT Score:550

by Abdulla » Tue Dec 16, 2008 6:38 pm

Thanks , got you.. but do you have another approach .. I mean by using the permutation formula??

Abdulla

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GMAT/MBA Expert

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 » Tue Dec 16, 2008 6:48 pm

The permutation formula is only used when you have n objects and you want to arrange some of those objects.
For example, you have 10 people and you want to seat (arrange) 4 of them in a row.

In the original question, we don't have that sort of situation.

In my opinion, there are few occasions when you have to use permutations on the GMAT. The Fundamental Counting Principle will do just fine.

The combinations formula, on the other hand, is definite must, especially if you are scoring in the 600+ range

Brent Hanneson - Creator of GMATPrepNow.com

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Wed Dec 17, 2008 1:57 am

Abdulla wrote:Thanks , got you.. but do you have another approach .. I mean by using the permutation formula??

IMO, the counting method with a pictorial representation, as done by brb88 is easier.

HT Helps

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