The posted prompt has a typo: the word SPENCE should actually written as SPENCER, as follows:
swerve wrote:In how many ways can the letters of the word SPENCER be arranged if the S and P must always be together and N and C must always be together?
A. 12
B. 24
C. 60
D. 120
E. 240
Since S and P must be together and N and C must be together, consider each pair a SEPARATE BLOCK in the arrangement, yielding the following list of 5 elements:
[SP], [NC], E, E, R
The number of ways to arrange 5 elements = 5! = 120.
Since SP can be reversed to PS -- doubling the number of arrangements -- we multiply by 2:
120*2 = 240.
Since NC can be reversed to CN -- again doubling the number of arrangements -- we again multiply by 2:
240*2 = 480.
The arrangement includes 2 identical E's.
When an arrangement includes IDENTICAL elements, we must divide by the number of ways each set of identical elements can be ARRANGED.
The reason:
When the identical elements swap positions, the arrangement doesn't change.
Here, we must divide by 2! to account for the two identical E's:
480/2! = 240.
The correct answer is
E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
