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The number of signals that can be generated by using 6 differently coloured flags, when any number of them may be hoisted at a time isA. 1956B. 1957C. 1958D. 1959

Answer» The singals can be made by using at a time one or more flags.
The total number of singals when r flags are used at a time from 6 flags is equal to the number of arrangements of 6, taking r at a time i.e., `""^(6)C_(r)xxr!`. Since r can take values 1, 2, 3, 4, 5, 6. Hence, the number of different signals that can be generated is
`sum_(r=1)^(6)""^(6)C_(r)xxr!""=6+30+120+360+720+720=1956`


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