Evaluate-5-6-mod-7-

Question Number 110595 by Aina Samuel Temidayo last updated on 29/Aug/20

Evaluate 5! ∙ 6! (\mod 7!)

Commented by Her_Majesty last updated on 29/Aug/20

{y o u}^{'} r e r i g h t

Commented by Aina Samuel Temidayo last updated on 29/Aug/20

Thanks but this is incorrect .

Commented by Her_Majesty last updated on 29/Aug/20

5! 6! = (17 + 1 / 7) 7! \Rightarrow a n s w e r i s 7! / 7 = 6! = 720

Commented by Aina Samuel Temidayo last updated on 29/Aug/20

Please I need a well - detailed solution

to the problem .

Commented by Her_Majesty last updated on 29/Aug/20

b u t i t i s!

\frac{5! 6!}{7!} = \frac{5! 6!}{6! \times 7} = \frac{5!}{7} = \frac{120}{7} = 17 + \frac{1}{7}

\Rightarrow

5! 6! = (17 + \frac{1}{7}) 7! = 17 \times 7! + \frac{7!}{7} = 17 \times 7! + 6!

\Rightarrow 6! = 720 i s t h e r e m a i n d e r