Question

A Signal is generated from 2 flags by putting
one flag above the other. If 4 flags of different
colours are available, how many different
signals can be generated?​

Answer 1

12 different signals can be generated.

Step-by-step explanation:

We are given that a signal is generated from 2 flags by putting  one flag above the other.

Also, 4 flags of different  colors are available.

As we have to generate two flags from the available 4 different colours flags which means that the number of ways in which 2 flags can be selected is given by;

The number of ways =  $^{4}C_2$

And here it should be noted that these two flag positions can be interchanged so we have to multiply 2 with the number of ways, i.e;

=  $2 \times ^{4}C_2$

=  $2 \times \frac{4!}{2! \times (4-2)!}$         {$\because ^{n}C_r = \frac{n!}{r! \times (n-r)!}$ }

=  $2 \times \frac{4!}{2! \times 2!}$

=  $2 \times \frac{4 \times 3 \times 2!}{2! \times 2!}$

=  $2 \times \frac{12}{2}$ = 12 ways

Hence, 12 different signals can be generated.

Answer 2

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