Permutations and Combinations question (1 Viewer)

[thoth1]

Just started this topic so go easy on me.

consider the letters in the word INCLUDE

How many seven letter words can be formed having the letters N and D separated by exactly two letters?

 

[kooliskool]

Well, think of it this way, you can only have 4 ways to have two spots for N and D separated by two letters:

e.g.:

N _ _ D _ _ _
_ N _ _ D _ _
_ _ N _ _ D _
_ _ _ N _ _ D

And arranging the letters separately (N and D first, then the 5 remaining letters) is:

2P2 and 5P5

So altogether that's 4*2P2*5P5=960

 

[muzeikchun852]

I will have a guess : 2! x 5! x 4 = 960 ?

 

[thoth1]

thats wrong according to the answers in cambridge 3 unit its 960.

 

[thoth1]

I will have a guess : 2! x 5! x 4 = 960 ?

this is correct. how did u get it?

 

[michaeljennings]

Well, think of it this way, you can only have 4 ways to have two spots for N and D separated by two letters:

e.g.:

N _ _ D _ _ _
_ N _ _ D _ _
_ _ N _ _ D _
_ _ _ N _ _ D

And arranging the letters separately (N and D first, then the 4 remaining letters) is:

2P2 and 4P4

So altogether that's 4*2P2*4P4=192

LOL incorrect answer doesnt do much for your sig ad

 

[tambam]

Well, think of it this way, you can only have 4 ways to have two spots for N and D separated by two letters:

e.g.:

N _ _ D _ _ _
_ N _ _ D _ _
_ _ N _ _ D _
_ _ _ N _ _ D

And arranging the letters separately (N and D first, then the 5 remaining letters) is:

2P2 and 5P5

So altogether that's 4*2P2*5P5=960

This is almost right, and a pretty goodd exxplanation, but I fixxed some bits up so it makes sense

 

[michaeljennings]

This is almost right, and a pretty goodd exxplanation, but I fixxed some bits up so it makes sense

You should tutor the tutor =)

 

[Peeik]

When I did this, I got 960....this is how I did it:

There are only 4 ways you can arrange the letters N and D such that they are exactly 2 spaces apart
i.e.
N _ _ D _ _ _
_ N _ _ D _ _
_ _ N _ _ D _
_ _ _ N _ _ D

Now if you look at those gaps, there are 5 of them right? So that means that there are 5 ! ways of arranging the remaining letters I-C-L-U-E provided N and D remain where that are. Therefore so far we have 4*5! But is not the final answer because N and D can be arrange in 2! ways.
i.e.
D _ _ N _ _ _
_ D _ _ N _ _
_ _ D _ _ N _
_ _ _ D _ _ N

Therefore you must multiply it by 2!.
i.e. 4*5!*2! = 960

Hopefully I'm correct and you understand my explanation

 

[kooliskool]

lols, excuse my counting mistake......, was watching a movie when I wrote this on my mobile phone.

 

[thoth1]

tnks for everyones help.

 

[kooliskool]

You are welcome, and good luck with your studies

 

[Drongoski]

lols, excuse my counting mistake......, was watching a movie when I wrote this on my mobile phone.

Don't worry about it. We all make mistakes from time to time. But I know you do know your maths.