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

The correct option is B

1956

Number of permutations of six signals taking 1 at a time = $6_{p_1}$

Number of permutations of six signals taking 2 at a time = $6_{p_2}$

Number of permutations of six signals taking 3 at a time = $6_{p_3}$

Number of permutations of six signals taking 4 at a time = $6_{p_4}$

Number of permutations of six signals taking 5 at a time = $6_{p_5}$

Number of permutations of six signals taking 6 at a time = $6_{p_6}$

$\therefore$ Total nubmer 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