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Find the number of ways in which 5A^(pri...

Find the number of ways in which `5A^(prime)s and 6B ' s` can be arranged in a row which reads the same backwards and forwards.

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We have letters A, A,A,A,A,B,B,B,B,B,B
According to the questionn, the middle letter must be A as even number of A's and even number of B's can be arranged symmetrically about the middle letter.
In that case we must have two A's and three B's on side.
A,A,B,B,B can be arranged on any of the sides in `(5!)/(2!xx3!)` ways.
Arranging A,A,B,B,B on one side of the middle place (6th place), its image about 6th place is done in a unique way.
Therefore, Number of ways`=(5!)/(2!xx3!)=10`
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