Perm & Combs (1 Viewer)

[Saturn WY15]

In how many ways can 5 boys and 3 women be arranged in circle if the women have to stand together. My answer was 480. (1* 2*2*5!) real answer is 720

 

[Saturn WY15]

Q2) Find the number of arrangements of the letter in the word pencils if e precedes i

 

[2xL]

1 ) 3! x 5! = 720
2) 6 x 5! = 720 please check.

 

[Carrotsticks]

1 ) 3! x 5! = 720
2) 6 x 5! = 720 please check.

How did you get your second answer?

Saturn, for 1) Group the women, so now there are 6 elements (5 men and the group). To arrange the 6 elements in a circle, there are 5! ways. Now arrange the women, so 3!. Hence we have 5! x 3!

Clue for #2: E is either before I, or after I. Nothing else.

 

[2xL]

well i used counting techniques for 2) _ _ _ _ _ _ _ and if e always precedes i, so theres 6 ways that can be done, and theres 5 slots left, so 5 factorial. .. :S

E I _ _ _ _ _
_ E I _ _ _ _
_ _ E I _ _ _
_ _ _ E I _ _
_ _ _ _ E I _
_ _ _ _ _ E I

and then 5 spaces for the other letters so 5 factorial?

 

[Carrotsticks]

Here's a simpler case for you.

Consider the word AIR.

How many ways can we arrange it such that R is before A? Remember, R is either before A, or after A.

 

[2xL]

Here's a simpler case for you.

Consider the word AIR.

How many ways can we arrange it such that R is before A? Remember, R is either before A, or after A.

How can R be after A . . . if it is before A... that confuses me. LOL.

RIA
RAI
IRA
?? Super confused.

 

[Carrotsticks]

How can R be after A . . . if it is before A... that confuses me. LOL.

EDIT!! OH I GET IT! HAHA

Haha, so what is your final answer for the AIR question?

 

[2xL]

Is the answer to b) 6! x 5! = 86400 ?

 

[Saturn WY15]

Answer for b is 2520

 

[Saturn WY15]

How did you get your second answer?

Saturn, for 1) Group the women, so now there are 6 elements (5 men and the group). To arrange the 6 elements in a circle, there are 5! ways. Now arrange the women, so 3!. Hence we have 5! x 3!

Clue for #2: E is either before I, or after I. Nothing else.

 

[2xL]

Answer for b is 2520

Ahh.

so if E is first, then E I _ _ _ _ _ and E _ I _ _ _ _ and E _ _ I _ _ _ and so forth, so 6 x 5!.
If E is second then _ E I _ _ _ _ and _ E _ I _ _ _ and so on so 5x5!.

Continue till E is 6th letter. _ _ _ _ _ E I.

Ansewr : 6 x 5! + 5 x 5! + 4 x 5! + 3 x 5! + 2 x 5! + 1 x 5! = 2520

 

[Saturn WY15]

Ahh.

so if E is first, then E I _ _ _ _ _ and E _ I _ _ _ _ and E _ _ I _ _ _ and so forth, so 6 x 5!.
If E is second then _ E I _ _ _ _ and _ E _ I _ _ _ and so on so 5x5!.

Continue till E is 6th letter. _ _ _ _ _ E I.

Ansewr : 6 x 5! + 5 x 5! + 4 x 5! + 3 x 5! + 2 x 5! + 1 x 5! = 2520

You are very good at this

 

[Carrotsticks]

You could have acquired that answer using 7!/2.

What I was getting at before was that E is either before or after so we just get the total then divide by 2.