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Suppose Roger has 4 identical green tennis balls and 5 identical red tennis balls. In how many ways can Roger arrange these 9 balls in a line so that no two green balls are next to each other and no three red balls are together (A) 8 (B) 9 (C) 11 (D) 12

 Suppose Roger has 4 identical green tennis balls and 5 identical red tennis balls. In how many ways can Roger arrange these 9 balls in a line so that no two green balls are next to each other and no three red balls are together (A) 8 (B) 9 (C) 11 (D) 12

Grade:12th pass

1 Answers

Dr Bhishma Hazarika
23 Points
4 years ago
Method I:
 
    (a) RGRGRGRGR  (5 red and 4 Green), As Identical balls this is one arragnement (1)
    (b) ___G____G____G____G(Four places for 5 red balls. 2 red balls wil be placed in one place and remaining one for one), So in 4 way it can be done (4)
    (c)G___G___G___G___ (fill up like option b in reverse order) again (4)
    (d) G___G___G___G (Three places for 5 red balls. 2 balls will be placed in any two places and remaining one will be placed in remaining place), so 3 way it can be done (3)
 
 So answer is 1+4+4+3=12
 
Method II:
 
 Let take the arrangement    ____R____R_____R_____R_____R____
 
So 4 green balls can be arranged in 6 places, so it is in    6 C4 way, but in some of the arrangement 3 red balls comes together.We can’t take those arrangement. those are GRRRGRGRG, GRGRGRRRG and GRGRRRGRG
 
So answer is   6 C4 -3=15-3=12

 
 

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