Question

Two blue flags, two red flags and four white flags are arranged in a line such that,

i] the flags at the two ends of the line are of the line are of different colours.

ii] no two adjacent flags or of the same colour.

In how many ways can this be done?

1. 8
2. 12
3. 16
4. 20

Answer 1

Correct Answer - Option 2 : 12

Calculation:

⇒ The four white flags could be arranged in two ways

⇒ W _ W _ W _ W _ W _ or _ W _ W _ W _ W

⇒ The two blue flags and two red flags can be arranged in the six spaces in ways i.e.

B B R R

B R B R

B R R B

R R B B

R B R B

R B B R

⇒ Total number of ways = 2 × 6 = 12.