Question

Permutations Question..?

How many combinations would a lock have if it had a 3-part combination and 5 stops with no stops repeated?

Can someone explain to me how to approach this question? Thanks!

Answer 1

i am going to guess \(5\times 4\times 3\) but i do not know what a "stop" is

Answer 2

I guess it means no numbers repeated?

Answer 3

@satellite73 a stop is when you switch directions on a rotatory combination lock

Answer 4

It harkens back to the days of telegraphs and such

Answer 5

@theequestrian

This is a a permutation. Do you know the formula for this? (hint: it has factorial symbols in it with variables r and n)

Answer 6

Yes. P(n,r)=n!/(n-r)! right?

Answer 7

wow typos everywhere by me today, "is a permutation" not "a a"

Answer 8

I just don't know how to tell which number is n and which is r

Answer 9

Types to choose from = n
Number chosen = r

Agree @satellite73 ? :-)

Answer 10

So n would be 5 and r would be 3?

Answer 11

And yes that is the right formula @theequestrian

Answer 12

hold the phone
a formula is nice, but thinking is also allowed
there are 5 choices for first "stop"
then 4 for the second (since you cannot repeat)
and finally 3 for the third (since you have used up the first two)
counting principle says the number of way to do this three things together is the product of each of the ways to do one of them. i.e.
\[5\times 4\times 3\]
don't get married to a formula, it may confuse the issue in different types of problems

Answer 13

don't worry about \(n\) and \(r\) etc. make sure to understand the problem and think through the solution

Answer 14

Okay, that makes sense. But since it is a '3 combination' wouldn't you have to multiply that answer from 5x4x3 by 3? Or not?

Answer 15

Wait, never mind. I understand now. Thanks a million both of y'all!