Verified answer

Răspuns:

Explicație pas cu pas:

1) numere de 4 cifre distincte cu 1 ; 2 ; 3 ; 4 =

= P₄ = 4! = 4·3·2·1 = 24

2) numere de 3 cifre distincte cu 1 ; 2 ; 3 ; 4 =

= 4·P₃ = 4·3! = 4·3·2·1 = 24

3) submultimi de 3 elemente cu {1 ; 2 ; 3 ; 4}

C₄³ = 4! / [3!·(4-3)!) = 4·3! /3! = 4

4) a) 30!/28! = 30·29·28!/28! = 30·29 = 870

   b) 5!/3! : P₆/P₄ = 5·4·3! / 3!  : 6!/4! =

= 20 : (6·5·4!/4!) = 20 : 30 = 2/3

   c) (P₇+P₈) : (P₅+P₆) = (7!+8!):(5!+6!) =

= (7!+8·7!) : (5! + 6·5!) = (7! · 9 ) : (5! ·7) =

= (9·7·6·5!) :(5!·7) = 9·6 = 54

  d) (A₅³ + A₄² ) : A₃² = [(5! / 3!) + (4!/2!)] : (3!/2!) =

= [5·4·3!/3! + 4·3·2/2 ] : (3·2/2) = (20+12):3 = 32/3

  e) C₇³ - C₇⁴ = [7!/3!·(7-3)!] - [7!/4!·(7-4)!] =

= 7! / (3! ·4!) - 7! / (4! ·3!) = 0