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Statistics

Count arrangements and selections (nPr and nCr)

Count how many ways to arrange or choose items from a group.

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A permutation counts the ways to pick items when order matters, such as awarding gold, silver and bronze. A combination counts the ways when order does not matter, such as picking a committee.

With 5 people and 3 places: nPr gives 5 × 4 × 3 = 60 ordered arrangements, and nCr gives 10 different groups.

Classic Graphing 84

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

  1. Type 5, then open the PROB menu (math, left, left). Choose nPr (option 2).

    5math◀◀2

  2. Type 3 and press enter.

    3enter

  3. For combinations, type 5, choose nCr (option 3) from the same menu, type 3 and press enter.

    5math◀◀33enter

You should see5 nPr 3 60 5 nCr 3 10

Classic Graphing 84 key reference

Classic Scientific 30

Start on the main screen: Press 2nd then mode (QUIT) to leave any menu or screen and return to the calculation screen.

  1. Type 5, then press prb and choose nPr (option 1). Type 3 and press enter.

    5prb13enter

  2. For combinations, type 5, press prb, choose nCr (option 2), type 3 and press enter.

    5prb23enter

You should see60 5 nCr 3 10

Classic Scientific 30 key reference

Natural Scientific 991

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

  1. Type 5, then SHIFT with × for nPr, then 3. Press =.

    5SHIFTnPr×3=

  2. For combinations, type 5, SHIFT with ÷ for nCr, then 3. Press =.

    5SHIFTnCr÷3=

You should seenPr shows 60 (5P3) and nCr shows 10 (5C3).

Natural Scientific 991 key reference

Natural Color Graphing

Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.

  1. Type 5, then open OPTN, move to its second page (F6) and choose PROB (F1). nPr is F2.

    5OPTNF6F1F23EXE

  2. Repeat for combinations with nCr (F3).

    5OPTNF6F1F33EXE

You should see5P3 60 5C3 10

Natural Color Graphing key reference

Classic CAS

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

  1. Open the Probability menu and choose nPr(. Give it 5 and 3 separated by a comma.

    menu535,3)enter

  2. For combinations, choose nCr( (option 2) in the same menu.

    menu525,3)enter

You should seenPr(5,3) 60 nCr(5,3) 10

Classic CAS key reference

RPN Scientific 15

Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.

  1. Key in 5, press ENTER, key in 3. Then press f and + for nPr (Py,x).

    5ENTER3fPy,x+

  2. For combinations, key in 5 ENTER 3 again and press g then + (Cy,x).

    5ENTER3gCy,x+

You should see10.0000 60.0000

RPN Scientific 15 key reference

RPN Advanced 42

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

  1. Open the PROB menu with shift then ×. Key in 5, press ENTER, then 3.

    ⇧PROB×5ENTER3

  2. Press the first menu key for combinations (CMB).

    Σ+

You should seex: 10.0000

The second menu key (PRM) gives permutations, 60.

RPN Advanced 42 key reference

RPN Power 48

Start on the main screen: Press ON to cancel what you are typing, then use the stack view. Open the MODE or VAR menu any time; the stack is always shown above the menu row.

  1. Key in 5, press enter, key in 3. Open the MTH menu with apps then F1 and move to its third page with nxt twice.

    5ENTER3APPSF1NXTNXT

  2. Press F3 for permutations (PERM).

    F3

You should see1: 60

F2 on that page is COMB, which gives 10.

RPN Power 48 key reference

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