GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Mar 2019, 20:43

### 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In how many ways can 10 identical tyres be distributed by the supplier

Author Message
TAGS:

### Hide Tags

Manager
Joined: 17 Oct 2016
Posts: 242
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)
In how many ways can 10 identical tyres be distributed by the supplier  [#permalink]

### Show Tags

19 Feb 2019, 08:02
3
00:00

Difficulty:

75% (hard)

Question Stats:

36% (01:47) correct 64% (01:52) wrong based on 59 sessions

### HideShow timer Statistics

In how many ways can 10 identical tyres be distributed by the supplier to 4 retail shops if any shop can get any number of tires?

A. $$\frac{13!}{10!3!}$$

B. $$\frac{10!}{7!3!}$$

C. $$\frac{10!}{7!4!}$$

D. $$\frac{11!}{7!4!}$$

E. $$\frac{13!}{10!4!}$$

_________________

_____________________
Chasing the dragon

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5380
Location: United States (CA)
Re: In how many ways can 10 identical tyres be distributed by the supplier  [#permalink]

### Show Tags

21 Feb 2019, 18:03
5
2
fitzpratik wrote:
In how many ways can 10 identical tyres be distributed by the supplier to 4 retail shops if any shop can get any number of tires?

A. $$\frac{13!}{10!3!}$$

B. $$\frac{10!}{7!3!}$$

C. $$\frac{10!}{7!4!}$$

D. $$\frac{11!}{7!4!}$$

E. $$\frac{13!}{10!4!}$$

We can let T be a tire, so we have:

TTTTTTTTTT

Since any of the 4 shops can receive any number of tires (including 0), let’s use 3 strokes (|) to separate the tires. For example, we can have:

TTT|TTT|TT|TT or TTTTTTTTTT|||

That is, in the first example, the first two shops each receive 3 tires, and the last two shops each receive 2 tires. In the latter example, the first shop receives all 10 tires while the other 3 shops receive none.

Therefore, the question becomes how many ways can we arrange 10 Ts and 3 strokes. The answer is:

13!/(10!3!)

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

##### General Discussion
Manager
Joined: 12 Apr 2011
Posts: 111
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21, Yale '21, INSEAD
GMAT 1: 670 Q50 V31
WE: Marketing (Telecommunications)
Re: In how many ways can 10 identical tyres be distributed by the supplier  [#permalink]

### Show Tags

20 Feb 2019, 03:21
1
2
fitzpratik wrote:
In how many ways can 10 identical tyres be distributed by the supplier to 4 retail shops if any shop can get any number of tires?

A. $$\frac{13!}{10!3!}$$

B. $$\frac{10!}{7!3!}$$

C. $$\frac{10!}{7!4!}$$

D. $$\frac{11!}{7!4!}$$

E. $$\frac{13!}{10!4!}$$

This is more of a formula based question. So better to memorize the below formula!

Number of ways of dividing 'n' identical objects into 'r' groups such that each group can contain any number of objects is given by

$$n+r-1_C_{r-1}$$

So,
The number of ways of dividing 10 identical tyres among 4 retail shops is

$$10+4-1_C_{4-1}$$

= $$13_{C_3}$$

= $$\frac{13!}{10!*3!}$$

Hence A is the correct answer.
_________________

Hit Kudos if you like what you see!

Manager
Joined: 23 Aug 2017
Posts: 85
Re: In how many ways can 10 identical tyres be distributed by the supplier  [#permalink]

### Show Tags

21 Feb 2019, 23:37
chetan2u

Could you please give a clear explanation .
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8997
Location: Pune, India
Re: In how many ways can 10 identical tyres be distributed by the supplier  [#permalink]

### Show Tags

22 Feb 2019, 06:29
fitzpratik wrote:
In how many ways can 10 identical tyres be distributed by the supplier to 4 retail shops if any shop can get any number of tires?

A. $$\frac{13!}{10!3!}$$

B. $$\frac{10!}{7!3!}$$

C. $$\frac{10!}{7!4!}$$

D. $$\frac{11!}{7!4!}$$

E. $$\frac{13!}{10!4!}$$

This is how you tackle distributing identical objects into distinct groups:
https://www.veritasprep.com/blog/2011/1 ... inatorics-–-part-1/

Check out the method 2 of question 2. It explains the most direct method of handling questions of this type. You don't need to remember any formulae in that case.
_________________

Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 20 Feb 2019
Posts: 5
Re: In how many ways can 10 identical tyres be distributed by the supplier  [#permalink]

### Show Tags

24 Feb 2019, 03:51
ScottTargetTestPrep wrote:
fitzpratik wrote:
In how many ways can 10 identical tyres be distributed by the supplier to 4 retail shops if any shop can get any number of tires?

A. $$\frac{13!}{10!3!}$$

B. $$\frac{10!}{7!3!}$$

C. $$\frac{10!}{7!4!}$$

D. $$\frac{11!}{7!4!}$$

E. $$\frac{13!}{10!4!}$$

We can let T be a tire, so we have:

TTTTTTTTTT

Since any of the 4 shops can receive any number of tires (including 0), let’s use 3 strokes (|) to separate the tires. For example, we can have:

TTT|TTT|TT|TT or TTTTTTTTTT|||

That is, in the first example, the first two shops each receive 3 tires, and the last two shops each receive 2 tires. In the latter example, the first shop receives all 10 tires while the other 3 shops receive none.

Therefore, the question becomes how many ways can we arrange 10 Ts and 3 strokes. The answer is:

13!/(10!3!)

Hi TTP,

I find your method of this explanation very innovative !!!!
Re: In how many ways can 10 identical tyres be distributed by the supplier   [#permalink] 24 Feb 2019, 03:51
Display posts from previous: Sort by