Question

Let $p$ be the number of permutations of AAAABBBC in which A's or B's occur together, then $p$ is

• A. divisible by 6
• B. even number
• C. divisible by 11
• D. divisible by 3

Answer 1

Answer: (B), (C)

The correct options are
B even number
C divisible by 11

1) AAAA as one unit; BBB, C separate
The number of permutations = $\frac{\lfloor 5}{\lfloor 3}=20$
2) BBB as one unit; AAAA, C separate
The number of permutations = $\frac{\lfloor 6}{\lfloor 4}=30$
3) AAAA, BBB as 2 units and C separate
The number of permutations $=\lfloor 3=6$
$p=20+30-6=44$
Hence, options B and C are correct.