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

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 ×(4 !) (C) 2 ×(4 !) (D) None of these

Tardigrade Admin · Accepted Answer

All strips are of different colours, then number of flags =3 !=6 When two strips are of same colour, then number of flags = 3 C1 ⋅ (3 !/2) ⋅ 2 C1=18 Total flags =6+18=24=4 !

Q. 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

$4!$

$3 \times (4!)$

$2 \times (4!)$

None of these

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 $= 6 + 18 = 24 = 4!$

Q. 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

4!

3×(4!)

2×(4!)