HP Forums - (12C Platinum) Combination Permutation

This program is from HP 12C Platinum Solutions Handbook.

To solve for Combination and Permutation the "Flags"
is use instead of manually go to [GTO] xxx
to go to specific program line.

Enter 0 to calculate Combination
Enter 1 to calculate Permutation

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Procedure:

0 [R/S] display 0 // for Combination

m [=] n [R/S] display Answer for Combination
----------------------------------------------------
1 [R/S] display 1 // for Permutation

m [=] n [R/S] display Answer for Permutation
----------------------------------------------------

Example:

5C3

0 [R/S] display 0 // calculate Combination

5 [=] 3 [R/S] display 10

-----------------------------------------------
11P4

1 [R/S] display 1 // calculate Permutation

11 [=] 4 [R/S] display 7920
-----------------------------------------------

Program: Combination Permutation (ALG Mode)

Code:

X=0

GTO 016

1

R/S

LSTx

-

X<>Y

=

X<>Y

n!

÷

X<>Y

n!

=

GTO 000

0

R/S

LSTx

-

X<>Y

=

X<>Y

n!

÷

X<>Y

n!

÷

LSTx

n!

=

Gamo

ALG program solution version II

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**Permutations: x P y

Procedure:

y [=] x [R/S] display answer

Example: 14 P 5

5 [=] 14 [R/S] display 240,240.00

Program: ALG mode

Code:

[-] [X<>Y] [=] [n!] [÷] [X<>Y] [n!] [=] [1/x]

----------------------------------------
**Combinations: x C y

Procedure:

y [=] x [R/S] display answer

Example: 14 C 5

5 [=] 14 [R/S] display 2002.00

Program: ALG Mode

Code:

[-] [X<>Y] [=] [n!] [x] [LSTx] [n!] [=] [÷] [X<>Y] [n!] [=] [1/x]

Gamo

Combinations and Permutation Version III
ALG mode program:

Program code is from HP-12C Platinum Solutions Handbook.

With this program both Combination and Permutation are combine into one program and the fist answer is Combination follow by Permutation.

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Procedure:

m [ENTER] n [R/S] display C [R/S] display P

--------------------------------------------------
Example: FIX 0

11C5 and 11P5

11 [ENTER] 5 [R/S] 462 [R/S] 55440

Answer: C=462 and P=55440
-------------------------------------------------
Program: ALG mode

Code:

006// [LSTx] [-] [X<>Y] [=] [X<>Y] [n!]

014// [÷] [X<>Y] [n!] [÷] [LSTx] [n!] [=] [R/S]

023// [R↓] [R↓] [=] [LSTx] [=] [LSTx] [-] [X<>Y] [=]

030// [X<>Y] [n!] [÷] [X<>Y] [n!] [=] [GTO 000]

Gamo

Combinations and Permutation Version IV
Program on RPN mode

mCn for Combination
mPn for Permutation

Where m can be larger than 69

For Permutation, n must be larger than 1 if user input n = 1
result will be wrong answers otherwise assumeing that if it is
mP1 then the answer is m

-----------------------------------------

Procedure: RPN mode FIX 0

Combination: Strat at begining of program: [GTO] 000 or [PRGM]

mCn

m [ENTER] n [R/S] ---> Answer

----------------------------------------

Permutation: Goto Line [GTO] 036

mPn

m [R/S] n [R/S] ---> Answer

---------------------------------------
Example: FIX 0

150C5

[PGRM] or [GTO] 000

150 [ENTER] 5 [R/S] display 591,600,030.
--------------------------------------
80P5

[GTO] 036

80 [R/S] display 80
5 [R/S] display 2,884,801,920.
---------------------------------------
For faster speed on Permutation of m < 70

[GTO] 075

m [R/S] n [R/S] ---> Answer
--------------------------------------
Program: RPN mode

Code:

001  -

002 LSTx

003 X≤Y

004 GTO 032

005 STO 0

006  1

007 STO 1

008  +

009 STO 2

010 CLx

011 X≤Y

012 GTO 014

013 GTO 034

014 Rv

015  1

016 RCL 1

017  +

018 STO 1

019 X≤Y

020 GTO 023

021 RCL 2

022 GTO 000

023 RCL 0

024 X<>Y

025  +

026 LSTx

027  ÷

028 RCL 2

029  x

030 STO 2

031 GTO 014

032 X<>Y

033 GTO 005

034  1

035 GTO 000  // End routine of Combination

--------------------

036 ENTER

037 STO 0

038 R/S

039 X≤Y

040 GTO 042

041 GTO 071

042 X≤Y

043 GTO 046

044  0

045  ÷

046  1

047 X≤Y

048 GTO 050

049 GTO 068

050 CLx

051 X≤Y

052 GTO 054

053 GTO 073

054  +

055  -

056  1

057  +

058  x

059 LSTx

060 RCL 0

061  1

062  -

063 X≤Y

064 GTO 068

065 GTO 066

066 Rv

067 GTO 056

068 Rv

069 Rv

070 GTO 000

071 n!

072 GTO 000

073  1

074 GTO 000  // End routine of Permutation

-------------------

075 ENTER

076 n!

077 X<>Y

078 R/S

079  -

080 n!

081  ÷ 

082 GTO 000  // End routine of fast Permutation

Gamo 1/2020