Question

Consider a flagpole with 10 spaces. There are 3 types of flags: Red flags occupy 1 space, blue and green flags occupy 2 spaces each. In how many ways can the 10 spaces of the flagpole can be covered with flags such that no spaces is empty.

Answer 1

Answer: There are 720 ways to do so.

Step-by-step explanation:

Since we have given that

Number of spaces in a flagpole = 10

Number of types of flag = 3

Number of spaces for red flag = 1

Number of spaces for green flag = 1

Number of spaces for blue flag = 1

We will use "Fundamental theorem of counting":

So, Number of ways that the 10 spaces of the flagpole can be covered with flags such that no spaces is empty is given by

$10\times 9\times 8\\\\=720$

Hence, there are 720 ways to do so.