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,