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!)
Answer: A