# Math Help - Probability Letter Arrangement

1. ## Probability Letter Arrangement

Hello there,

If somebody could assist me with this question I'd be very appreciative:

"How many ways are there to arrange the letters:"

1) SEARCH
2) FORMULAE
3) HOROSCOPES
4) DIFFERENTIATE

Am I right in thinking the answers are:

1) 6! / 1!
2) 8! / 1!
3) 10! / (3!2!) - taking the duplicate o's and duplicate s's as factorials in order
4) 13! / (3!2!2!) - taking duplicate e's, f's and i's as factorials in order

Also, are those answers in the format required or would numerical answers be suited? It's been a while so apologies for any obvious mistakes or misunderstandings.

Regards,

2. Originally Posted by rel85
"How many ways are there to arrange the letters:"
1) SEARCH
2) FORMULAE
3) HOROSCOPES
4) DIFFERENTIATE
Am I right in thinking the answers are:
1) 6! / 1!
2) 8! / 1!
3) 10! / (3!2!) - taking the duplicate o's and duplicate s's as factorials in order
4) 13! / (3!2!2!) - taking duplicate e's, f's and i's as factorials in order
Also, are those answers in the format required or would numerical answers be suited? It's been a while so apologies for any obvious mistakes or misunderstandings.
First, all are correct.
As to the format of the answer, its is the way I want students to leave the answer. Because it clearly shows understanding.

I say leaveing the first two as just $6!~\&~8!$ is best.

But all of this depends on your instructor.

3. Originally Posted by Plato
First, all are correct.
As to the format of the answer, its is the way I want students to leave the answer. Because it clearly shows understanding.

I say leaveing the first two as just $6!~\&~8!$ is best.

But all of this depends on your instructor.
I see, thank you very much!