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

Answer 1

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 ⁶P₅ and with all 6 flags ⁶P₆ .
∴ Total number of signals = ⁶P₁ + ⁶P₂ + ⁶P₃ + ⁶P₄ + ⁶P₅ + 6P₆
= 6 + 30 + 120 + 360 + 720 + 720 = 1956