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

Question

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!}

ScottTargetTestPrep · Accepted Answer

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!)

Answer: A

eabhgoy · Answer

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.

Debashis Roy · Answer

chetan2u

Could you please give a clear explanation .

KarishmaB · Answer

This is how you tackle distributing identical objects into distinct groups: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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.

kumarankitabes · Answer

Hi TTP,

I find your method of this explanation very innovative !!!!

Kinshook · Answer

Asked: 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?

Number of ways = (10+4-1)C(4-1) = 13C3 = 13!/10!3!

IMO A

Oppenheimer1945 · Answer

Using star and bars for unrestricted distribution:

10+4-1 C 4-1=13C3
A)

ivycation2024 · Answer

Next level ! perfect approach and explaination, 10000000000000000000000 kudos!

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

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

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