House owner decides to repaint the house. He want to make a particular wall in the hall, decorative and decides to put 7 coloured horizontal stripes in it. The seven colours he chose is Violet, Indigo, Blue, Green, Yellow, Orange, Red. As Blue, Violet and Indigo are very similiar shades he decides not to put them next to each other. How many different patterns do he have to choose from?
Pick one:  A) 6! - (5!×3!)  B) 7! - (5!×2!)  C) 6! - (2!×4!)  D) 7! - (5!×3!)  E) 7! - (6!×3!)
The answer is not direct. Problem require us to find the number of different arrangements of 7 coloured stripes. The constraints we have is that B, V and I should not come next to each other. We can find the answer by substracting the number of arrangments in which B, V and I come together from the total arrangements of 7 stripes. Arrangements in which B, V and I come together: we can consider B, V and I as a single object, but remembering that there can be 3! different such objects. For each BVI object we can arrange BVI, R, O, Y, G in 5! Ways. There four in total there is 5! × 3! Ways of arranging 7 stripes with B, V, I together. And total arrangement of 7 stripes is 7!. Therefore the answer we need is D. (7! -( 5!×3!))
<result>D</result>
House owner decides to repaint the house. He want to make a particular wall in the hall, decorative and decides to put 7 coloured horizontal stripes in it. The seven colours he chose is Violet, Indigo, Blue, Green, Yellow, Orange, Red. As Blue, Violet and Indigo are very similiar shades he decides not to put them next to each other. How many different patterns do he have to choose from?