# The number of different signals which can be given from 6 flags of different colours taking one or more at a time,

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

Solution:

(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 $=\frac{6 !}{5 !}+\frac{6 !}{4 !}+\frac{6 !}{3 !}+\frac{6 !}{2 !}+\frac{6 !}{1 !}+6 !$

$=6+30+120+360+720+720$

$=1956$