count based based on 2 columns

I have 3 columns
column a is a horse race id
column 2 is a horse name from that race
column 3 is a P or N
I have used 2 horses from the first race and 2 from the second and stripped out all the other columns.

what I need is shown ..I need a formula to count the number of N and P
each horse in each race shown in col d and col e

it must be able to drag down for thousands of rows

thanks very much

race_no horse PN
20150219CHELM_6:40 Ada Lovelace P
20150219CHELM_6:40 Ada Lovelace N
20150219CHELM_6:40 Ada Lovelace P
20150219CHELM_6:40 Ada Lovelace N
20150219CHELM_6:40 Ada Lovelace N
20150219CHELM_6:40 Olney Lass N
20150219CHELM_6:40 Olney Lass N
20150219CHELM_6:40 Olney Lass P
20150219CHELM_6:40 Olney Lass P
20150219CHELM_7:10 Caledonia Laird P
20150219CHELM_7:10 Caledonia Laird N
20150219CHELM_7:10 Welsh Gem N
20150219CHELM_7:10 Welsh Gem N

race_no horse PN PCOUNT NCOUNT
20150219CHELM_6:40 Ada Lovelace P 2 3
20150219CHELM_6:40 Ada Lovelace N 2 3
20150219CHELM_6:40 Ada Lovelace P 2 3
20150219CHELM_6:40 Ada Lovelace N 2 3
20150219CHELM_6:40 Ada Lovelace N 2 3
20150219CHELM_6:40 Olney Lass N 2 2
20150219CHELM_6:40 Olney Lass N 2 2
20150219CHELM_6:40 Olney Lass P 2 2
20150219CHELM_6:40 Olney Lass P 2 2
20150219CHELM_7:10 Caledonia Laird P 1 1
20150219CHELM_7:10 Caledonia Laird N 1 1
20150219CHELM_7:10 Welsh Gem N 0 2
20150219CHELM_7:10 Welsh Gem N 0 2

To best describe or illustrate your problem you would be better off attaching a dummy workbook. The workbook should contain the same structure and some dummy data of the same type as the type you have in your real workbook - so, if a cell contains numbers & letters in this format abc-123 then that should be reflected in the dummy workbook.

To attach a file to your post,
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Thanks for the file

why would you want to repeat the same entry, with the same count, multiple times? Wouldnt it make more sense to just show unique entries, with a count for that 1?

The formulas to give what you showed would be
=COUNTIFS($A$2:$A$14,A17,$B$2:$B$14,B17,$C$2:$C$14,"p")
=COUNTIFS($A$2:$A$14,A17,$B$2:$B$14,B17,$C$2:$C$14,"n")

Happy to help