Question

3 – Quantos anagramas a palavra CARINHO possuem as vogais juntas?

4 – Da palavra CONQUISTA :
Quantos anagramas podemos formar?
Quantos são os anagramas que começam com vogal?
Quantos são os anagramas que começam e terminam com consoantes?
Quantos são os anagramas que possuem as vogais juntas?
Quantos anagramas possuem a sílaba CON

Answer 1

$\boxed{\begin{array}{l} \rm 3)~\sf\underbrace{\sf\boxed{\sf AIO}CRNH}_{ P_3\cdot P_5}\\\sf P_3\cdot P_5=3!\cdot5!\\\sf 3\cdot2\cdot1\cdot5\cdot4\cdot3\cdot2\cdot1=720~anagramas\end{array}}$

$\boxed{\begin{array}{l}\rm 4)\\\tt a)~\sf\underbrace{\sf CONQUISTA}_{P_9}=9!=362880\\\tt b)~\sf\underbrace{\sf\boxed{\sf O}CNQUISTA}_{4\cdot P_8}=4\cdot 8!=161280\\\tt c)~\sf\underbrace{\sf \boxed{\sf C}ONQUISA\boxed{\sf T}}_{ 5\cdot P_7\cdot 4}=20\cdot 7!=100800\\\tt d)~\sf\underbrace{\sf\boxed{\sf OUIA}CNQST}_{ P_4\cdot P_6}=4!\cdot 6!=17280\\\tt e)~\sf\underbrace{\sf \boxed{\sf CON}QUISTA}_{P_7}=7!=5040\end{array}}$