Solutions of Question 9 of Exercise 6.2 of Unit 06: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.
How many signals can be given by six flags of different colors when any number of them used at a time?
We have to form signals using the six colors of the six flags.
If each signal consist of one color then total number of signals $=^6 P_1=6$.
If each signal consist of two color then total number of signal $s=^6 P_2=30$.
If each signal consist of three color then total number of signals $=^6 P_3=120$.
If each signal consist of four color then total number of signals $=^6 P_4=360$.
If each signal consist of five color then toțal number of signals $=^6 P_5=720$.
If each signal consist of six color then total number of signals $=^6 P_6=720$.
Hence the total number of signals are: $6+30+120+360+720+720=1956$.