Code:

.orig x3000
;Clear registers
and r0, r0, #0
and r1, r1, #0
and r2, r2, #0
and r3, r3, #0
and r4, r4, #0
and r6, r6, #0
and r7, r7, #0
;parameters
add r0, r0, #4
add r1, r1, #2
ld r6, stackBase ;beginning of stack
;Push param1 and param2 on stack
add r6, r6, #-2
str r0, r6, #1
str r1, r6, #0
jsr NchooseR ;NchooseR( r0, r1 )
lea r0, eopMssg
puts
halt
stackBase .fill xFD00
eopMssg
.stringz "\n\nEnd of processing..."
NchooseR ;NchooseR( r0, r1 )
add r6, r6, #-2
str r2, r6, #0
str r7, r6, #1
;load param1 and param2
ldr r0, r6, #3 ;r0 <- param1
ldr r1, r6, #2 ;r1 <- param2
not r3, r1
add r3, r3, #1 ;-param2
add r3, r0, r3 ;param1-param2
brnz NchooseRSpecialCase
add r1, r1, #0 ;check if param2 is zero
brz NchooseRSpecialCase
add r0, r0, #-1
br NchooseRGeneral
NchooseRSpecialCase ;r = 0
add r0, r0, #0 ;n < 0
brn NchooseRReturn
and r0, r0, #0 ;zero out register
add r0, r0, #1 ;return 1
br NchooseRReturn
NchooseRGeneral
add r6, r6, #-2
str r0, r6, #1 ;push param1 - 1
str r1, r6, #0 ;push param2
jsr NchooseR ;r0 <- NchooseR( param1 - 1, r1 )
add r6, r6, #2 ;pop param1 - 1 and param2
add r2, r0, #0 ;r2 <- NchooseR( param1-1, param2 )
ldr r0, r6, #2 ;r0 <- param1-1
ldr r1, r6, #1 ;r1 <- param2
add r0, r0, #0 ;r0 <- param1 ;**used to be #-1
add r1, r1, #-1 ;r1 <- param2 - 1
;push variables on stack
add r6, r6, #-2
str r0, r6, #1 ;push param1
str r1, r6, #0 ;push param2-1
jsr NchooseR ;NchooseR( param1-1, param2-1 )
add r6, r6, #2
add r0, r0, r2 ;r0 <- NchooseR( n-1, r ) + NchooseR( n-1, r-1 )
NchooseRReturn
ldr r2, r6, #0
ldr r7, r6, #1 ;restore r7
add r6, r6, #2 ;pop locals and parameters
ret
.end