Question

2) Calcule:
a) 6!
b)5!-4!
c)12!3!/15!
d)4*2!​

Answer 1

Explicação:

A)

$6! = 6 \times (6 - 1) \times (6 - 2) \times (6 - 3) \times (6 - 4) \times (6 - 5) \times (6 - 6)! = \\ 6 \times 5 \times 4 \times 3 \times 2 \times 1 \times 0! = 720$

B)

$5! - 4! \\ 5 \times (5 - 1) \times (5 - 2) \times (5 - 3) \times (5 - 4) \times (5 -5)! = 5 \times 4 \times 3 \times 2 \times 1 \times 0! = 120 \\ 4! = 4 \times (4 - 1) \times (4 - 2) \times (4 - 3) \times (4 - 4)! = 4 \times 3 \times 2 \times 1 \times 0! = 24 \\ 5! - 4! = 120 - 24 = 96$

$\frac{12! \times 3!}{15!} = \frac{12! \times 3!}{3! \times 5!} = \frac{3!}{3!} \times \frac{12!}{5!} = 1 \times \frac{12 \times 11 \times 10 \times9 \times 8 \times 7 \times 6 \times 5! }{5!} = \frac{5!}{5!} \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 = \\ 1 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 = 3.991.680$

D)

$4 \times 2! = 4 \times 2 = 8$