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  • Determine the total number of signals that can be made by six distinct coloured flags when any number of them can be used in any signal.  Option:

Determine the total number of signals that can be made by six distinct coloured flags when any number of them can be used in any signal.

 

Option: 1

1616


Option: 2

1863


Option: 3

1956


Option: 4

2053


Answers (1)

best_answer

Given that,

There are 6 different colored flags.

The possible number of cases to find the total number of flags is

Case I: 

When only one flag is used. 

The Number of signals made is given by,

\begin{aligned} &{ }^6 P_1=\frac{6 !}{(6-1) !}\\ &{ }^6 P_1=6 \end{aligned}

Case II: 

When only two flags are used. 

Number of signals made is given by,

\begin{aligned} &{ }^6 P_2=\frac{6 !}{(6-2) !}\\ &{ }^6 P_2=30 \end{aligned}

Case III: 

When only three flags are used. 

The number of signals made is given by,

\begin{aligned} &{ }^6 P_3=\frac{6 !}{(6-3) !}\\ &{ }^6 P_3=120 \end{aligned}

Case IV: 

When only four flags are used. 

The number of signals made is given by,

\begin{aligned} &{ }^6 P_4=\frac{6 !}{(6-4) !}\\ &{ }^6 P_4=360 \end{aligned}

Case V: 

When five flags are used. 

The number of signals made is given by,

\begin{aligned} & { }^6 P_5=\frac{6 !}{(6-5) !} \\ & { }^6 P_5=720 \end{aligned}

Case VI: 

When six flags are used. 

The number of signals made is given by,

\begin{aligned} &{ }^6 P_6=\frac{6 !}{(6-6) !}\\ &{ }^6 P_6=720 \end{aligned}

Therefore, the number of ways the signals can be formed is 6 + 30 + 120 + 360 + 720 + 720 = 1956.

 

 

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