Find the no. of ways you can fill a 3*3 grid(with 4 corners defined as a,b,c,d)if you have 3 white marbles,6 black marbles

• have to put 9 marbles in nine places...and out of them 3 are of one type and 6 are of another type
  so answer is 9!/(3!*6!) = 84 ways
• 11 years agoHelpfull: Yes(35) No(1)
• 84 ways
  
  There are three main possible ways of arranging the marbles -
  
  1) BBB , BBB, WWW
  
  Arranging these three set of marbles in three rows = 3
  by keeping www in top , middle and bottom row one by one.
  
  2) BBW , BBW , BBW
  
  Arranging these three set of marbles in three rows = (3!/2!)*(3!/2!)*(3!/2!)=3*3*3 =27
  
  3)BWW , BBW , BBB
  
  Arranging these three set of marbles in three rows = 3!*(3!/2!)*(3!/2!)*(3!/3!) = 54 as all three groups are different from each other.
  
  Total arrangements = 54 + 27 + 3 =84
• 11 years agoHelpfull: Yes(13) No(0)
• Ans: 84
  
  =========================================================================
  nCr = C(n,r)
  
  Filling 9 Place with 3 white ball = C(9,3).
  Remaining place is 9-3=6, thus filling rest of the place = C(9-3, 6) = 1
  
  Total = C(9,3)*C(9-3,6) = 84*1 = 84
• 11 years agoHelpfull: Yes(12) No(0)
• Just find the ways of putting 3 white marbles at 9 possible places.
  possible ways = 9C3= 9*8*7/6 = 84 ways
• 11 years agoHelpfull: Yes(8) No(1)
• In addition to answer of Garima.Just find the ways of putting 3 white marbles or 6 black marbles at 9 possible places.
  possible ways = 9C3 or 9C6= 9*8*7/6 = 84 ways (nCr=nCn-r)
• 11 years agoHelpfull: Yes(4) No(1)
• total marbles are 9 so, 9! ways and 3 are common and 6 are common...
  so,
  9! / 3!*6! =9*7*8/6 =12*7=84 ways...
• 9 years agoHelpfull: Yes(2) No(0)
• possible ways 9C6=84
• 7 years agoHelpfull: Yes(0) No(0)
• Firstly the question is not complete..
  please ans this question in
  1) 9C3
  2) 6C3
  3) 9C3+6C3
  4) (9C3+6C3)/3!
  in this
• 5 years agoHelpfull: Yes(0) No(0)