3 card poker help

Hi,

Just wondering if anyone could help me as I cant seem to get my head around this logic. I want to know the probability of getting 3 cards that are greater than 9 (Ten, Jack, Queen, King, Ace) but do not contain the any hand higher (So no pairs, three of a kind, etc..). I know I could calculate all all hands where there are only these high cards - minus each other type of hand but would take me to work out each amount.

Wondering if anyone could provide some simple maths for me as this would be a great help!

Thanks in advance

Choose 3 of 5 ranks
Subtract the 3 ways to make a straight

There are 4*4*4 suits
Subtract the 4 ways to make a flush

(combin(5,3)-3)*(4^3-4) = 420
Did this on my phone so double check the answer

Checked this and is the same as the answer I got but a lot more compact. Thank you!!