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Question

Messages are conveyed by arranging 4 white, 1 blue and 3 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 transmitted if exactly six flags are used is

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Solution

We will consider the following cases :

Case I - when 4 alike and 2 others alike flags are used (4 white and 2 red ),
then no. of signals =6!4!2!=15

Case II -when 4 alike and 2 others different flags are used (4 white, l red and 1 blue ) then no. of signals =6!4!=30

Case III - when 3 alike and 3 others alike flags are used (3 white, 3 red ) then no. of signals =6!3!3!=20

Case IV - when 3 alike and 2 other alike and 1 different flags are used (3 white, 1 blue. 2 red or 3 red, 1 blue, 2 white)
then no. of signals =2×6!3!2!=120

Total =15+30+20+120=185

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