Question

The total number of flags with three horizontal strips, in order, that can be formed using $2$ identical red, $2$ identical green and $2$ identical white strips, is equal to

• A. $4!$
• B. $3 \times(4 !)$
• C. $2 \times(4 !)$
• D. None of these

Answer 1

Answer: (A)

All strips are of different colours, then number of flags
$=3 !=6$
When two strips are of same colour, then number of flags
$={ }^{3} C_{1} \cdot \frac{3 !}{2} \cdot{ }^{2} C_{1}=18$
Total flags $=6+18=24=4 !$