Messages are conveyed by arranging four white, one blue and three red flags on a pole. Flags of the same colour are alike. If a message is transmitted by the order in which the colours are arranged. T

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Messages are conveyed by arranging four white, one blue and three red flags on a pole. Flags of the same colour are alike. If a message is transmitted by the order in which the colours are arranged. The total number of messages that can be conveyed if exactly six flags are used is

TestHub · Accepted Answer

4 alike and 2 others alike ( 4 W , 2 R ) = 4 ! 2 ! 6 ! ​ 4 alike and 2 others different ( 4 W , 1 R , 1 B ) = 4 ! 6 ! ​ 3 alike, 3 others alike ( 3 W , 3 R ) − 3 ! 3 ! 6 ! ​ 3 alike, 2 others alike, 1 different ( 3 W , 1 B , 2 R , (or) 3 R , 1 B , 2 W ) = 2 C 1 ​ × 3 ! 2 ! 5 ! ​

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