In how many different orders can five runners finish a race if no ties are allow

iohanetc 2021-09-09 Answered
In how many different orders can five runners finish a race if no ties are allowed?

Want to know more about Exponential growth and decay?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

aprovard
Answered 2021-09-10 Author has 20530 answers

Definitions
Definition permutation (order is important):
\(\displaystyle{P}{\left({n},{r}\right)}={\frac{{{n}!}}{{{\left({n}-{r}\right)}!}}}\)
Definition combination (order is not important):
\(C(n,r)=\left(\begin{array}{c}n\\ r\end{array}\right)=\frac{n!}{r!(n-r)!}\)
with \(n!=n \cdot (n-1) \cdot \ldots \cdot 2 \cdot 1\)
Solution
The order of the runners is important, thus we need to use the definition of permutation.
We will select 5 runners from the 5 runners (as we want an ordering of all runners).
n=5
r=5
Evaluate the definition of a combination:
\(\displaystyle{P}{\left({5},{5}\right)}={\frac{{{5}!}}{{{\left({5}-{5}\right)}!}}}={\frac{{{5}!}}{{{0}!}}}={5}\ne{120}\)
Results:
120

Not exactly what you’re looking for?
Ask My Question
4
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-11-16
Two runners start a race at the same time and finish in a tie. Prove that at some time during the race they have the same speed. [Hint: Consider \(\displaystyle{f}{\left({t}\right)}={g}{\left({t}\right)}-{h}{\left({t}\right)}\) , where and are the position functions of the two runners.
asked 2021-08-20
This is for Discrete Math.
Three horses A,B and C, can finish a race in how many ways? (ties are possible)
1) 10
2) 15
3) 9
4) 12
5) 13
asked 2021-02-25
We will now add support for register-memory ALU operations to the classic five-stage RISC pipeline. To offset this increase in complexity, all memory addressing will be restricted to register indirect (i.e., all addresses are simply a value held in a register; no offset or displacement may be added to the register value). For example, the register-memory instruction add x4, x5, (x1) means add the contents of register x5 to the contents of the memory location with address equal to the value in register x1 and put the sum in register x4. Register-register ALU operations are unchanged. The following items apply to the integer RISC pipeline:
a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.
b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.
c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.
d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.
Hint for (d): Give a pair of instruction sequences where the RISC pipeline has “more” instructions than the reg-mem architecture. Also give a pair of instruction sequences where the RISC pipeline has “fewer” instructions than the reg-mem architecture.
asked 2021-05-05
If there are 7 bands and 3 floats, in how many different ways can they be arranged?
asked 2021-12-18
In how many ways can 8 people be seated in a row if a.) there are no restrictions on the seating arrangement(answer is \(\displaystyle{8}!={40},{320}\)) , b.) persons A and B must sit next to each other? (Answer: 10,080) , c.) there are 4 men and 4 women and no 2 men or 2 women can sit next to each other? (Answer: 1,152) , d.) there are 5 men and they must sit next to one another? (Answer: 2,880) , e.) there are 4 married couples and each couple must sit together? (Answer: 384). I need to see the steps to solve questions 10b to 10e. I quickly looked through the corresponding chapter on combinatorial analysis and I went over topics such as the multinomial theorem, the basic principle of counting, the binomial theorem, and representing the number of possible combinations of n objects taken r at a time as "n choose r" .
asked 2021-08-06
2 points) Page Turner loves discrete mathematics. She has 8 "graph theory" books, 6 books about combinatorics, and 4 "set theory" books.
How many ways can she place her discrete mathematics books on the same shelf in a row if:
a) there are no restrictions.
b) graph theory books are next to each other but the others could be anywhere on the shelf.
c) books are organized by their topic (same kinds are next to each other).
asked 2021-04-13
As depicted in the applet, Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring is compressed 5.00 m from its equilibrium position, and a glass sits 19.8m from her outstretched foot.
a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.
...