knight247 wrote:Mrs. Smith has been given film vouchers. Each voucher allows the holder to see a film without charge. She decides to distribute them among her four nephews so that each nephew gets at least two vouchers. How many vouchers has Mrs. Smith been given if there are 120 ways that she could distribute the vouchers?
A. 13
B. 14
C. 15
D. 16
E. more than 16
To guarantee that each nephew receives at least 2 vouchers, first give each of the 4 nephews EXACTLY 2 vouchers.
This accounts for 8 of the vouchers.
Now that each nephew has 2 vouchers, there are no restrictions on how the REMAINING vouchers can be distributed.
Thus, 120 = the number of ways to distribute the REMAINING vouchers.
We can plug in the answers and use the SEPARATOR METHOD to count the number of possible distributions.
(For an explanation of the SEPARATOR METHOD, please check here:
https://www.beatthegmat.com/experts-any- ... 82307.html.)
Answer choice C: 15 vouchers.
Remaining vouchers after the first 8 have been distributed = 15-8 = 7.
Let the 7 vouchers = VVVVVVV.
Since these 7 vouchers can be distributed among up to 4 nephews, we need 3 separators: |||.
Number of ways to arrange the 10 elements VVVVVVV||| = 10!/7!3! = 120.
Success!
The correct answer is
C.
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
