January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score. January 21, 2019 January 21, 2019 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52296

Three small cruise ships, each carrying 10 passengers, will dock
[#permalink]
Show Tags
07 Jul 2015, 02:04
Question Stats:
43% (02:15) correct 57% (01:57) wrong based on 164 sessions
HideShow timer Statistics
Three small cruise ships, each carrying 10 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random; each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out? A. 270 B. 450 C. 2,700 D. 4,500 E. 27,000 Kudos for a correct solution.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



CEO
Joined: 20 Mar 2014
Posts: 2636
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Three small cruise ships, each carrying 10 passengers, will dock
[#permalink]
Show Tags
07 Jul 2015, 04:01
Bunuel wrote: Three small cruise ships, each carrying 10 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random; each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
A. 270 B. 450 C. 2,700 D. 4,500 E. 27,000
Kudos for a correct solution. Number of ways 3 ships can go to 3 ports = 3! =6 Let ship A goes to dock A . Thus, the number of ways of selecting 2 winners out of 10 passengers = 10C2 = 45 Let ship B goes to dock B . Thus, the number of ways of selecting 1 winner out of 10 passengers = 10C1 = 10 Let ship C goes to dock C . Thus, the number of ways of selecting 1 winner out of 10 passengers = 10C1 = 10 Thus the total number of arrangements possible = 6*45*10*10 = 27000, thus E is the correct answer.



Retired Moderator
Joined: 29 Apr 2015
Posts: 841
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: Three small cruise ships, each carrying 10 passengers, will dock
[#permalink]
Show Tags
07 Jul 2015, 04:59
Bunuel wrote: Three small cruise ships, each carrying 10 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random; each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
A. 270 B. 450 C. 2,700 D. 4,500 E. 27,000
Kudos for a correct solution. First Cruise Ship: 2 out of 10, order doesn't matter / no repetition > 10!/8!*2! = 45 Second Cruise Ship: 1 out of 10, order doesn't matter / no repetition > 10!/9! = 10 Second Cruise Ship: 1 out of 10, order doesn't matter / no repetition > 10!/9! = 10 Alltogether: 45*10*10 = 4500 Answer D
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2726
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: Three small cruise ships, each carrying 10 passengers, will dock
[#permalink]
Show Tags
07 Jul 2015, 08:32
Bunuel wrote: Three small cruise ships, each carrying 10 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random; each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
A. 270 B. 450 C. 2,700 D. 4,500 E. 27,000
Kudos for a correct solution. @PORT A: The gifts have to be given to 2 out of 10 members who can be selected in 10 C2 ways = 45 ways Please Note: Here the arrangement doesn't come into picture because both the gift values are same. If the gift values were different then it would have required the arrangement of Gifts between the 2 selected candidates out of 10@PORT B:The gift has to be given to 1 out of 10 members who can be selected in 10 C1 ways = 10 ways @PORT C:The gift has to be given to 1 out of 10 members who can be selected in 10 C1 ways = 10 ways Since there are 3 different ships carrying different sets of 10 people each so the group of 10 people taking gifts at different ports can also be arranged and the arrangements of three Ships at three ports = 3! = 6 Total Ways to give gifts on all three ports = 45*10*10*6 = 27000 ways Answer: Option E
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Math Expert
Joined: 02 Sep 2009
Posts: 52296

Re: Three small cruise ships, each carrying 10 passengers, will dock
[#permalink]
Show Tags
13 Jul 2015, 03:04
Bunuel wrote: Three small cruise ships, each carrying 10 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random; each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
A. 270 B. 450 C. 2,700 D. 4,500 E. 27,000
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION: This problem features four separate decisions. In other words, you must answer four separate questions: (1) Which ship docks at which port? (2) Who are the two people who receive the two gift certificates at Port A? (3) Who receives the one gift certificate at Port B? (4) Who receives the one gift certificate at Port C? The first of these decisions is a permutation, because "order matters." In other words, switching any of the port assignments results in a new arrangement. Since the gift certificates are worth different amounts at different ports, the specific way in which we assign ships to ports matters. Thus, we calculate the number of permutations of the 3 ships over the 3 ports as 3! = 6. The second decision is a combination, because "order does not matter." You do not care about the sequence in which you choose the two winners. You only care about who has won. Since there are 2 winners and 10  2 = 8 losers out of a pool of 10 contestants at Port A, we can write the number of combinations as 10!/(2!8!) = 45. Finally, the third and fourth decisions are very simple combinations. You have 10 choices for who receives the certificate at Port B, and separately you have 10 choices for who receives the certificate at Port C. The decisions are sequential, and they are made independently. As a result, the numbers of possibilities are multiplied at the end of the problem. The total number of ways the gift certificates can be given out is therefore 3!*10!/(2!8!)*10*10 = 27,000. Answer: E.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



NonHuman User
Joined: 09 Sep 2013
Posts: 9454

Re: Three small cruise ships, each carrying 10 passengers, will dock
[#permalink]
Show Tags
20 Apr 2018, 01:12
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Three small cruise ships, each carrying 10 passengers, will dock &nbs
[#permalink]
20 Apr 2018, 01:12






