The number of signals that can be sent by 6 flags of different colours taking one or more at a time is
Question:

The number of signals that can be sent by 6 flags of different colours taking one or more at a time is

(a) 63

(b) 1956

(c) 720

(d) 21

Solution:

Number of signals possible with one flag is 6.

Number of signals possible with 2 flags is 6P2 .

Number of signals possible with 3 flags is 6P3 .

Similarly with 4 flags 6P4, 5 flags is 6Pand with all 6 flags 6P.

∴ Total number of signals = 6P1 + 6P6P+  6P6P+ 6P

= 6 + 30 + 120 + 360 + 720 + 720 = 1956

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