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

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

Permutations and Combinations

Solution:

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