Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2601:30 AM EDT
-02:30 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
23 Oct 2020, 00:00
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
25% (02:48) correct
75%
(02:32)
wrong
based on 75
sessions
History
Date
Time
Result
Not Attempted Yet
A bag contains 6 chips numbered 1-6 respectively. If these chips are distributed among 4 students such that each student gets at-least one chip, how many different ways the chips can be distributed?
a. 480
b. 1080
c. 1200
d. 1560
e. 1800
a. 480
b. 1080
c. 1200
d. 1560
e. 1800
23 Oct 2020, 22:10
Kudos
Bookmarks
I chose the method below as this is what came to my mind first. There may be a shorter approach.
Case 1: One person (Say A) takes 3 chips and each of the others take 1 chip each
Number of ways that A chooses 3 out of 6 chips = \(^6C_3 = 20\)
Number of ways that B chooses 1 out of the remaining 3 chips = \(^3C_1 = 3\)
Number of ways that C chooses 1 out of the remaining 2 chips = \(^2C_1 = 2\)
D gets the last chip in 1 way.
The number of ways to do the above = 20 * 3 * 2 = 120
There are 4 ways in which A or B or C or D could get 3 chips.
Therefore Total ways for case 1 = 120 * 4 = 480
Case 2: Two persons (Say A and B) take 2 chips each and each of the others take 1 chip each
Number of ways that A chooses 2 out of 6 chips = \(^6C_2 = 15\)
Number of ways that B chooses 2 out of the remaining 4 chips = \(^4C_2 = 6\)
Number of ways that C chooses 1 out of the remaining 2 chips = \(^2C_1 = 2\)
D gets the last chip in 1 way.
The number of ways to do the above = 15 * 6 * 2 = 180
The number of combinations of 2 people getting 2 chips each and the others getting 1 each = \(^4C_2 = 6\)
(AB, AC, AD, BC, BD or CD)
Therefore Total ways for case 2 = 180 * 6 = 1080
Total Possible ways = 480 + 1080 = 1560
Option D
Arun Kumar
Case 1: One person (Say A) takes 3 chips and each of the others take 1 chip each
Number of ways that A chooses 3 out of 6 chips = \(^6C_3 = 20\)
Number of ways that B chooses 1 out of the remaining 3 chips = \(^3C_1 = 3\)
Number of ways that C chooses 1 out of the remaining 2 chips = \(^2C_1 = 2\)
D gets the last chip in 1 way.
The number of ways to do the above = 20 * 3 * 2 = 120
There are 4 ways in which A or B or C or D could get 3 chips.
Therefore Total ways for case 1 = 120 * 4 = 480
Case 2: Two persons (Say A and B) take 2 chips each and each of the others take 1 chip each
Number of ways that A chooses 2 out of 6 chips = \(^6C_2 = 15\)
Number of ways that B chooses 2 out of the remaining 4 chips = \(^4C_2 = 6\)
Number of ways that C chooses 1 out of the remaining 2 chips = \(^2C_1 = 2\)
D gets the last chip in 1 way.
The number of ways to do the above = 15 * 6 * 2 = 180
The number of combinations of 2 people getting 2 chips each and the others getting 1 each = \(^4C_2 = 6\)
(AB, AC, AD, BC, BD or CD)
Therefore Total ways for case 2 = 180 * 6 = 1080
Total Possible ways = 480 + 1080 = 1560
Option D
Arun Kumar
General Discussion
23 Oct 2020, 22:45
Kudos
Bookmarks
QuantMadeEasy
Apart from the way shown above, a quick method would be..
Let us distribute chips without any restrictions = \(4^6\)....Each chip can go to any of the 4 students.
Now this total has ways in which the chips have been distributed between just 3 of them or just 2 of them or just 1.
We have to subtract these ways..
To cater for above colored portion, let us SUBTRACT -
1) Amongst 3 of them..
Without restriction - 4C3*3^6
But these ways subtract the ways it is distributed between 2 and 1 more than ONCE.
example - Let us look at just A.
So A will be part of ABC, ABD and ACD, making him part of group of 2s twice.
ABC will give AB and AC
ABD will give AB and AD
ACD will give AC and AD
That is AB, AC, AB, AD, AC and AD
Thus the group of 2s is getting subtracted TWICE. Also, A will be considered single thrice, once in each of ABC, ABD and ACD. So it is getting subtracted thrice.
To cater for above colored portion, let us ADD
2) Between 2 of them
So let us add the way it will be distributed between two to cater for the EXTRA subtraction. => \(4C2*2^6\)
But again A will be part of AB, AC and AD, so A will get added THREE times, leading to NO subtraction at all.
To cater for above colored portion, let us SUBTRACT
3) Just 1
\(4C1*1^6\)
Answer --
\(4^6-4C3*3^6+4C2*2^6-4C1*1^6\)
\(= 4096-4*729+6*64-4*1\)
\(=4096-2916+384-4\)
\(=1560\)
D
