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# The number of signals that can be formed using 6 flags of different colours taking 1 or more flags at a time is ?

$\begin{array}{1 1} 63 \\ 720 \\ 1956 \\ 6^6 \end{array}$

No. of signals with one flag $=6$
No. of signals with 2 flags = $^6P_2=30$
No. of signals with 3 flags = $^6P_3=120$
No. of signals with 4 flags = $^6P_4=360$
No. of signals with 5 flags = $^6P_5=6!=720$
No. of signals with 6 flags = $^6P_6=720$
Total no. of signals = $720+720+360+120+30+6$
$=1956$

edited Dec 20, 2013