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How many different signal can be giving using any number of flag from flag 4 of the different colour

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The signals can be made by using one or more flags at a time. Hence, by the fundamental principal of addition, the total number of signals
`=.^(4)P_(1)+.^(4)P_(2)+.^(4)P_(3)+.^(4)P_(4)`
`=4+(4xx3)+(4xx3xx2)+(4xx3xx2xx1)`
`=4+12+24+24=64`
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