Question

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

Answer 1

(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

∴ Total number of signals $=\frac{6!}{5!}+\frac{6!}{4!}+\frac{6!}{3!}+\frac{6!}{2!}+\frac{6!}{1!}+6!$

$$\begin{gathered} =6+30+120+360+720+720 \\ =1956 \end{gathered}$$