Combinations and permutations: Difference between revisions

=={{header|Bracmat}}==

Bracmat cannot handle floating point numbers. Instead, this solution shows the first 50 digits and a count of the digits that are not shown.

<lang Bracmat>( ( C

= n k coef

. !arg:(?n,?k)

& (!n+-1*!k:<!k:?k|)

& 1:?coef

& whl

' ( !k:>0

& !coef*!n*!k^-1:?coef

& !k+-1:?k

& !n+-1:?n

)

& !coef

)

& ( P

= n k result

. !arg:(?n,?k)

& !n+-1*!k:?k

& 1:?result

& whl

' ( !n:>!k

& !n*!result:?result

& !n+-1:?n

)

& !result

)

& 0:?i

& whl

' ( 1+!i:~>12:?i

& div$(!i.3):?k

& out$(!i P !k "=" P$(!i,!k))

)

& 0:?i

& whl

' ( 10+!i:~>60:?i

& div$(!i.3):?k

& out$(!i C !k "=" C$(!i,!k))

)

& ( displayBig

=

. @(!arg:?show [50 ? [?length)

& !show "... (" !length+-50 " more digits)"

| !arg

)

& 5 50 500 1000 5000 15000:?is

& whl

' ( !is:%?i ?is

& div$(!i.3):?k

& out$(str$(!i " P " !k " = " displayBig$(P$(!i,!k))))

)

& 0:?i

& whl

' ( 100+!i:~>1000:?i

& div$(!i.3):?k

& out$(str$(!i " C " !k " = " displayBig$(C$(!i,!k))))

)

);</lang>

Output:

<pre>1 P 0 = 1

2 P 0 = 1

3 P 1 = 3

4 P 1 = 4

5 P 1 = 5

6 P 2 = 30

7 P 2 = 42

8 P 2 = 56

9 P 3 = 504

10 P 3 = 720

11 P 3 = 990

12 P 4 = 11880

10 C 3 = 120

20 C 6 = 38760

30 C 10 = 30045015

40 C 13 = 12033222880

50 C 16 = 4923689695575

60 C 20 = 4191844505805495

5 P 1 = 5

50 P 16 = 103017324974226408345600000

500 P 166 = 35348749217429427876093618266017623068440028791060... (385 more digits)

1000 P 333 = 59693262885034150890397017659007842809981894765670... (922 more digits)

5000 P 1666 = 68567457572556742754845369402488960622341567102448... (5976 more digits)

15000 P 5000 = 96498539887274939220148588059312959807922816886808... (20420 more digits)

100 C 33 = 294692427022540894366527900

200 C 66 = 72697525451692783415270666511927389767550269141935... (4 more digits)

300 C 100 = 41582514632585647447833835263264055802804660057436... (32 more digits)

400 C 133 = 12579486841821087021333484756519650044917494358375... (60 more digits)

500 C 166 = 39260283861944227552204083450723314281973490135301... (87 more digits)

600 C 200 = 25060177832214028050056167705132288352025510250879... (115 more digits)

700 C 233 = 81032035633395999047404536440311382329449203119421... (142 more digits)

800 C 266 = 26456233626836270342888292995561242550915240450150... (170 more digits)

900 C 300 = 17433563732964466429607307650857183476303419689548... (198 more digits)

1000 C 333 = 57761345531476516697774863235496017223394580195002... (225 more digits)</pre>