Question

A shipping company devises a messaging consisting of 9 flags hung in a line. Howmany different messages are possible if communication is constructed from a set of4 white, 3 red, and 2 blue flags. Note that ordering of the colors matters, but thatflags of the same color are indistinguishable from one another.

Answer 1

Answer: 1260

Step-by-step explanation:

The number of permutation of n things in which 'a' things are like , 'b' things are like and so on.. is given by :-

$\dfrac{n!}{a!\ b!....}$

Given : A shipping company devises a messaging consisting of 9 flags hung in a line.

Then, the number of different possible messages constructed from a set of 4 white, 3 red, and 2 blue flags will be :-

$\dfrac{9!}{4! 3!2!}\\\\=\dfrac{9\times8\times7\times6\times5\times4!}{4! 3\times2\times2}\\\\=1260$

Hence, the number of different possible messages constructed from a set of 4 white, 3 red, and 2 blue flags= 1260