Page 58 - الرياضيات المتقدمة كتاب الطالب للصف 11 الفصل 2

b Gb ^ Æ{j b {6 1.b d?Wb ç 2;N x- 'b X?cb f.[ gb Ÿ zB y2b

,1Vfa yb Y U1Ne

permutations ^ ¹C ± ] ±»C< R ± ¤Ð­ C Õ 7 C F:94 »P0: ±

\= ±b ± ¤½±b M± Û ] (› ˜½±b M± Û ]6 Z C ± û0 ±
combinations ( • ½œ’ ­ E ¹C ± ³P b ±
œ
œ
¹P4 ± ²ÒR1 ( ½ — ½œ • ›’ “½ — ›’ ² ³R/ E ¹C ± ³P b ±

factorial of a number
ÎC8 C G9 ¦[yU r a q cx, a 40-i . fa

Pascal’s triangle \= ±b ±Ò permutations ^ ¹C ± –C< = R Ò RjC;4 ± »C= C Ãbhb: ± ±Q c;4Ù

` K P ± ´±º E R3 ´C;= ÒR ± `= ´C 4 ± –ÏC4 ± ^7; ± ¤^ ³P74 E P ´C7= 2 d R<3 combinations
Binomial theorem ´C=9: Ò EÛ R ± »ÒR: ± ´C:9 Y6 ²b C ± _9 ´C= ¼»±b –E= ±»b ± E P;< ± d
˜³R6/: ± E= ÒR 8 ˆ± ³»C ±
D= R ÐC ±º¯ `8 Ò –_< R= »C= „± D= R ÐC ±º¯ \= ±b RjC;4 ± »C= ± E=9: c:

˜^ ¹C c: »C= „± E=9: ÐA –CÕ:< »C= „±
¤d Š± û=jb ± ÃC ± `8: –\= ±b ±Ò ^ ¹C ± `= ÌR6 ± N=hb Ò

˜`Û=4 D= R d C< = R Ò RjC;4 ± »C= „ E7 R d ^ ¹C ± y

ÒÓ
¤d d ±Ò ¶ –² –­ ËR M± ` `=Ø R ^ ¹C E ÍC; ÎC : ± ^= c94 5656
˜“² – ¶’ – “¶ – ²’ – “­ – ¶’ – “¶ – ­’ – “­ – ²’ – “² – ­’

Õ
Õ
G= –­ _ „Ò­ ² »C= ± E7 R ` ² _ „Ò­ ­ »C= ± E7 R û9 E C ± ÑQ d
˜CÕ:< D= R ± Ðb8
C Õ =g» Ðb8= P ±Ò V »C= ± D Ò C E; d ¿C ­ E ÍC; ÐC ±º¯ ] Q
–Ÿ –ž – –œ –› ¤ÏC »MC `=: R: ± ¿C M± `= `: –a gC Ðb8= R ¬ V Ò C<
Ò­ “T=gR ± DgC ’ ›Ò “T=g»’ œ Ò­ “T=gR ± DgC ’ œÒ “T=g»’ › ¤C; P Ðb8 Э `8:

˜O ¯ ˜˜˜ –“T=gR ± DgC ’ ›Ò “T=g»’  Ò­ “T=gR ± DgC ’ Ò “T=g»’ ›
˜C< = R »C „± `=4 Q M± ÐÒ¹ RjC;4 ± »C= „ E7 R d \= ±b ± y

¤d d ±Ò ¶ –² –­ ËR M± ` `=Ø R \= ±b »C= „ ÌR µ ÍC; Õ :
Õ
Õ
˜­ _ „Ò­ ² »C= ± C< 6 d ² _ „Ò­ ­ »C= ± E7 R Я ˜“¶ –²’ –“¶ –­’ –“² –­’
Õ
˜„Ò­ Ñ»C= ± Û_ ÔQ ± ËR ± ` R3; ± W5 ² –­ `=Ø R ± c9 ^0 Э b _<: ±
³R8 ± \ R `8 –`= „ E ` ³RgC2 ± ³R8 ± \ R ÐÛb8 ¤\= ±b ± c9 R ¬ ÎC : Ò
³R8 ± \ R ` `= Ø „ »C= ± C ¹»­ ±º¯ ˜X7 `=Ø „ ` ÐÛb8 E= C/ ± ³RgC2 ±
C: »C ÔQ ± D= R ± _< –E= C/ ± ³RgC2 ± ³R8 ± E 4 d E »C/:9 ³RgC2 ±

`=Ø ± »C= ± C;;8:= –Ÿ –ž – –œ –› `=: R E ± Ðb ± ÐC ±º¯Ò ˜a=
˜O ¯ ˜˜˜ Ò­ “ž –›’ Ò­ “ –›’ Ò­ “œ –›’
Ð
“² • ½ ­’ ³»bj d d ± E R ± ³»C 4 ± ]6 û= C Õ 1 ­ ³P b ± ÑQ d _94 Ëb
_< b Ò ˜` K P ± ´±º Íb86 Ãb; ± ±Q ` Íb86: ± c: Ò –D b N= j ¹P Ð G=
˜´„C: „± ²C E9= b CÕ7 „ a P ] M