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2m white counters and 2n red counters are arranged in a straight line with (m + n) counters on each side of a central mark. The number of ways of arranging the counters, so that the arrangements are symmetrical with respect to the central mark is

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a

m+nCm

b

2m+2nC2m

c

12(m+n)!m!n!

d

none of these

answer is A.

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Detailed Solution

m+n counters on one side can be arranged (m+n)!m!n! ways. For each arrangement on one side, corresponding arrangement on the other side is just one as arrangements are symmetrical. Hence, the total number of arrangements is (m+n)!m!n!=m+nCm
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2m white counters and 2n red counters are arranged in a straight line with (m + n) counters on each side of a central mark. The number of ways of arranging the counters, so that the arrangements are symmetrical with respect to the central mark is