Question

Calcule os arranjos e combinações a seguir
a) A4,3=
b) A5,4=
c) A7,2 - A4,3=
d) C5,3=
e) C7,5=
f ) C6,2=

Answer 1

Aₙₓ = n! / (n-x)!

Cₙₓ = n! / (n-x)!x!

a) A4,3=

= 4!/(4 - 3)!

= 4!/1!

= 4!

= 24

b) A5,4=

= 5!/(5 - 4)!

= 5!/1!

= 5!

= 120

c) A7,2 - A4,3=

= 7!/(7-2)! - 4!/(4-3)!

= 7!/5! - 4!/1!

= 7 . 6 . 5!/5! - 4!

= 7 . 6 - 24

= 42 - 24

= 18

d) C5,3=

= 5!/(5-3)!3!

= 5!/2!3!

= 5 . 4 . 3!/2!3!

= 5 . 4/2

= 5 . 2

= 10

e) C7,5=

= 7!/(7 - 5)!5!

= 7!/2!5!

= 7 . 6 . 5!/2!5!

= 7 . 6/2

= 7 . 3

= 21

f ) C6,2=

= 6!/(6-2)!2!

= 6!/4!2!

= 6 . 5 . 4!/4!2!

= 6 . 5/2

= 3 . 5

= 15