Difficult to phrase question to do with number of possibilities

If there were 4 destinations and you had to visit each one in a single journey. What is the number of possible paths you could take to reach them all?

Would the calculation be 4⁴?

Reply 1

Zacken

Original post by BhagwanNoBhool

If there were 4 destinations and you had to visit each one in a single journey. What is the number of possible paths you could take to reach them all?

Would the calculation be 4⁴?

Could you provide a picture of the question?

Reply 2

Notnek

Original post by BhagwanNoBhool

If there were 4 destinations and you had to visit each one in a single journey. What is the number of possible paths you could take to reach them all?

Would the calculation be 4⁴?

Call the destinations A, B, C, D

then a possible path could be BCAD or ADBC

Consider how many options ther are for the first letter... then the second letter etc.

Reply 3

BhagwanNoBhool

Original post by Zacken

Could you provide a picture of the question?

It's not a written question, but maths problem to do with a computer program for my course work

Original post by notnek

Call the destinations A, B, C, D

then a possible path could be BCAD or ADBC

Consider how many options ther are for the first letter... then the second letter etc.

Would there be 4² for each letter? So 64 paths in total?

Reply 4

Notnek

Original post by BhagwanNoBhool

Would there be 4² for each letter? So 64 paths in total?

You seem to be guessing or using some incorrect method without thinking.

ACBD
DACB
etc.

How can there be 16 choices for the first letter?

Reply 5

BhagwanNoBhool

Original post by notnek

You seem to be guessing or using some incorrect method without thinking.

ACBD
DACB
etc.

How can there be 16 choices for the first letter?

Sorry, I misinterpreted what you were saying.
There are 4 choices for each letter.

So 4 paths for the first one,
A
B
C
D

Then 4 times as many for the next.
AA CA
AB CB
AC CC
AD CD
BA DA
BB DB
BC DC
BD DD

Would it always be four times as many for the next letter?

Reply 6

Notnek

Original post by BhagwanNoBhool

Sorry, I misinterpreted what you were saying.
There are 4 choices for each letter.

So 4 paths for the first one,
A
B
C
D

That's correct.

To visit all four destinations you need the four letters to be different e.g. ACDB or CDBA. That means the second letter cannot be the same as the first letter.

So if there are 4 choices for the first letter, how many choices are there for the second?

This is all assuming I'm interpreting your question correctly. Some of your replies suggest that your actual question may be different.

Reply 7

BhagwanNoBhool

Original post by notnek

No you're correct with the question, sorry I wasn't thinking with the repeating letter ones. For the second there are 3 choices remaining, 2 for the third and 1 for the last.

Reply 8

Notnek

Original post by BhagwanNoBhool

No you're correct with the question, sorry I wasn't thinking with the repeating letter ones. For the second there are 3 choices remaining, 2 for the third and 1 for the last.