Question

The number of permutations of all the letters $AAAABBBC$ in which all the $A's$ appear together in the block of $3$ letters, is-

• A. 44
• B. 50
• C. 60
• D. 89

Answer 1

Answer: (A)

$P =$ All $A' s$ together $=\frac{5 !}{3 !}$,
$Q =$ all $B$ 's together $=\frac{6 !}{4 !}$
$n ( P \cap Q )=3 ! \Rightarrow n ( P \cup Q )$
$=\frac{5 !}{3 !}+\frac{6 !}{4 !}-3 !=44$