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Question

# Messages are conveyed by arranging four white, one blue, and three red flags on a pole. Flags of the same color are alike. If a message is trasmitted 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

A
45
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B
65
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C
125
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D
185
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Solution

## The correct option is D 185We will consider the following casesCaseFlagsNo. of signals4 alike and 2 others alike4 white and 2 red6!4!2!=154 alike and 2 others different4 white, 1 red and 1 blue6!4!=303 alike and 3 other alike3 white, 3 red6!3!3!=203 alike and 2 other alike and 1 different3 white, 1 blue, 2 red or 3 red, 1 blue, 2 white2C1×6!3!2!=120Total185

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