probability

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

sud21: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sat Nov 12, 2011 3:21 am; Thanked: 1 times; Followed by:2 members

probability

by sud21 » Sat Jan 28, 2012 10:21 pm

How many arrangements of the digits 1, 2, 3, 4, and 5 are there, such that 2 and 4 are not adjacent?

Quote

Source: Beat The GMAT — Problem Solving | Sat Jan 28, 2012 10:21 pm

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

by rijul007 » Sat Jan 28, 2012 11:05 pm

sud21 wrote:How many arrangements of the digits 1, 2, 3, 4, and 5 are there, such that 2 and 4 are not adjacent?

Total number of arrangements = 5!

Let us assume that 24 is a sigle element
Number of arrangements of 1, 24,3,5 = 4!
Nuumber of arrangemtns of 1, 42,3,5 = 4!

Number of arrangements such that 2,4 are not adjacent = 5! - 2*4! = 120 - 48 = 72

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jan 03, 2018 4:10 pm

sud21 wrote:How many arrangements of the digits 1, 2, 3, 4, and 5 are there, such that 2 and 4 are not adjacent?

We can use the following formula:

Total number of arrangements = # ways with 2 and 4 adjacent + # ways with 2 and 4 not adjacent

The total number of arrangements is 5! = 120

Next we can determine the number of arrangements when 2 and 4 are adjacent. We can make the numbers 2 and 4 one placeholder, such that there are 4 total positions or 4! = 24. However, we must include that we can arrange the 2 and 4 in 2! = 2 ways. So, the total number of ways is 24 x 2 = 48.

Therefore, the number of ways with 2 and 4 not adjacent is 120 - 48 = 72

Scott Woodbury-Stewart
Founder and CEO
[email protected]