Question

How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F.

Probability and combinatorics
ANSWERED
asked 2021-05-17
How many permutations of three items can be selected from a group of six? Use the letters A,
B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F.

Answers (1)

2021-05-18
Definition permutation (order is important):
\(P_{n,r}=\frac{n!}{(n-r)!}\)
Definition combination (order is not important):
\(C_{n,r}=\frac{n!}{r!(n-r)!}\)
with \(n!=n\cdot(n-1)\cdot...\cdot2\cdot1\)
Given:
\(n=6\)
\(r=3\)
We need to use permutations:
\(P_{6,3}=\frac{6!}{(6-3)!}=\frac{6!}{3!3!}=\frac{6\cdot5\cdot...\cdot1}{3\cdot2\cdot1}=6\cdot5\cdot4=120\)
All ways in which we can select 3 outcomes from the group of three items B,D and F:
BBB, BBD, BDB, DBB, BBF, BFB, FBB, BDF, BFD, DDD, DDB, DBD, BDD, DDF, DFD, FDD, DBF, DFB, FFF, FFB, FBF, BFF, FFD, FDF, DFF, FBD, FDB
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

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 2021-09-15
How many five-letter sequences are possible that use the letters q, u, a, k, e, s at most once each?
asked 2021-05-05
If John, Trey, and Miles want to know how’ | many two-letter secret codes there are that don't have a repeated letter. For example, they want to : count BA and AB, but they don't want to count“ doubles such as ZZ or XX. Jobn says there are 26 + 25 because you don’t want to use the same letter twice; that’s why the second number is 25.
‘Trey says he thinks it should be times, not plus: 26-25, Miles says the number is 26-26 ~ 26 because you need to take away the double letters. Discuss the boys’ ideas, Which answers are correct, which are not, and why? Explain your answers clearly and thoroughly, drawing ‘on this section’s definition of multiptication.. -
asked 2021-05-30
There are three women and four men in a group of seven people. If three people are selected from the total of seven, find the following: i)What are the total possible outcomes for this selection? ii)How many ways can two women and one man be selected? iii)What is the probability of selecting two women and one man?
...