The number of different signals which can be given from 6 flags of different colours taking one or more at a time,
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
(a) 1958
(b) 1956
(c) 16
(d) 64
(b) 1956
Number of permutations of six signals taking 1 at a time = 6P1
Number of permutations of six signals taking 2 at a time = 6P2
Number of permutations of six signals taking 3 at a time = 6P3
Number of permutations of six signals taking 4 at a time = 6P4
Number of permutations of six signals taking 5 at a time = 6P5
Number of permutations of six signals taking all at a time = 6P6
$\therefore$ Total number of signals $=\frac{6 !}{5 !}+\frac{6 !}{4 !}+\frac{6 !}{3 !}+\frac{6 !}{2 !}+\frac{6 !}{1 !}+6 !$
$=6+30+120+360+720+720$
$=1956$
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