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72 \ (2)(3) = 6 Pant 2 53 k n n n 1 2 k n n ... n n - PowerPoint PPT Presentation

Sep 29, 2022 •516 likes •756 views

, ,Pz3 EP f- z shirts - pxSSILsnsz.Si3lpxsI-lPl.lslshirt1pant11shit2@P1.s 72 \ (2)(3) = 6 Pant 2 53 k n n n 1 2 k n n ... n n k 1 2 k 1 k we 22-52 26 ' 16 1600 5 . gb za = = - . 63 E I

  3. , ,Pz3 EP f- z shirts ✓ - pxSSILsnsz.Si3lpxsI-lPl.lslshirt1pant11shit2@P1.s €72 \ (2)(3) = 6 Pant 2 53 k n n n 1 2 k n ⋅ n ⋅ ... ⋅ n ⋅ n k 1 2 k −1 k we

  4. 22-52 26 ' 16 1600 5 . gb za = = - . 63 E I 2 0 E . - - a , , , 23 lo total I b e , , ways = f # options for 5) 2) ( # options for of . 3=1217 t I ) ( 2 I ) ( 6 7 = t = I 2 19 factors 2 : = - proper

  5. =/3 I EG 3-63-6 . . . .

  6. S M C ∣ S ∪ M ∪ C ∣ = ∣ S ∣ + ∣ M ∣ + ∣ C ∣ = 3 + 4 + 2 = 9 n , n , ... n k 1 2 k n + n + ... + n 1 2 k -

  7. An BI At tf BI =/ IA UBI I - 25 TO 40 x 50 = 40 + 25 − x ⇒ x = 15

  8. : 1333J - I 3 333 of 2 3 . - - - 3 - . Mutt 3 : , , 5 200 51,5-2 - of 5 malt - : - - - , 66J :/ 15-1,15-2 15%6 15 malt of . - - : , 333+200-66=14677 Total :

  9. ! 5 -3-21 I = 5- ⇒ diff 473£ Go -3 I 5- =

  10. n ! = n ⋅ ( n − 1) ⋅ ... ⋅ 2 ⋅ 1 k n n ! P ( n , k ) = ( n − k )! i÷n 5⋅4⋅3⋅2⋅1 5! 5 ⋅ 4 ⋅ 3 = = 2⋅1 2! . - n ! n n ! P ( n , n ) = = n ! 0!

  11. Pilar RADI D 3! = 6 Dz AD , A Dz D , ! R of D : how 2 permutations many , RADAR . . - . . DADD : 3 !

  12. I M : ! 11 4 : - ssss 'D 4714114 ( 1111 4 : " repeat Tnepeasted Ps 2 repeated PP :

  13. ! BB 2 A Y DOG of characters the do times How many other next each to , appear order : any :O . : :* : : : I

  14. but gray ;;t rotated - ÷ , . 5 ! , 4 ! = I

  15. 5! 2! 3! = 6 5! 3! 2! 3! 5! 5 ⋅ 4 ⋅ 3! = = 10 2!3! 2 ⋅ 1 ⋅ 3!

  16. k n n ! ( k n ) = ( n − k )! k ! n k n ) n ) = n − k ( k ( n − k k { A , B , C , D , E } C 5 ) C II - - - C : ) ( it -

  17. O O O 00 - - 8 ) ( 3 9 ) ( 5 8 )( 5 9 ) ( 3

  18. 8 − k k ways (at least 4 b) = ways (4 b) + ways (5 b) + ways (6 b) + ways (7 b) + ways (8 b) 8 )( 4 9 ) 8 )( 3 9 ) 8 )( 2 9 ) 8 )( 1 9 ) 8 )( 0 9 ) ( 4 ( 5 ( 6 ( 7 ( 8 = + + + +

  19. Find I I } ) . ( 42 ) - . 43 ( 13 . I # ¥ ÷÷ #÷¥÷ I . .

  20. EE ' EE 4¥ . . . 9. 4-4.4-4.4=19-457 g. I Y I - 44k¥17

  21. = ( ntl ) It 2T th - . . . I tht th S = - - - proof - Ht nth S= I t - - . - combinatorial Show LHS and ( I ) KHS count ABCDE - same quantity AB 4 AI.AD.AE , BE 3 BD BE , , 2 CE CD , DE I

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