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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
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B
even number
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C
divisible by 11
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D
divisible by 3
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Solution

The correct options are
B even number
C divisible by 11
1) AAAA as one unit; BBB, C separate
The number of permutations = 53=20
2) BBB as one unit; AAAA, C separate
The number of permutations = 64=30
3) AAAA, BBB as 2 units and C separate
The number of permutations =3=6
p=20+306=44
Hence, options B and C are correct.

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