Find the number of ways you can fill a 3 x 3 grid (with 4 corners defined as a, b, c, d), if you
have 3 white marbles and 6 black marbles

• The area of the grid is = 9.
  Now, No. of ways we can arrange 3 white balls in 9 places = 9c3.
  and 6 black balls in (9-3) = 6 places = 6c6 = 1.
  So total = 9c3 * 1 = 9c3.
  
  In another way,
  
  No ways we can arrange 6 black balls in 9 places = 9c6 = 9c3
  and no ways 3 white balls in (9-6) places = 3c3 = 1
  
  No. of ways we can arrange 3 white balls and 9 black balls in 3x3 grid is = 9c3*1 = 9c3
• 8 years agoHelpfull: Yes(17) No(0)
• 9 block are available
  so either we place black first or white first
  if white first then its i 9c3*6c6
  if black first then 9c6*3c3
  so total ways 9c3*6c6+9c6*3c3=2*84=168
• 8 years agoHelpfull: Yes(8) No(4)
• ans>>
  Total places = 9
  Number of marbles = 9, out of which 3 marbles are white and 6 marbles are black
  So the possible number of arrangements are
  9! / ( 3! * 6! ) =84
• 8 years agoHelpfull: Yes(7) No(0)
• As the marbles are identical the required answer is 9C3or 9C6 i.e. we can start filing the Grid either with white or black marbles.
  
  We have 3 identical white marbles which can be placed in 9 blocks in 9C3 ways and the rest 6 blocks can be filled with 6 white marbles so the required ways of filling the grid is 9C3.
  
  Even if we start filling the 3x3 grid with black marbles the required permutation is 9C6.
  ANS = 9C3 = 9C6 = option A
• 8 years agoHelpfull: Yes(3) No(0)
• The answer is 9 c 3 or 9 c 6. i.e 9 c 3 + 9 c 6.
• 8 years agoHelpfull: Yes(2) No(4)
• Option A should be 9c3 not 8c3 because the answer is 9c3.
• 8 years agoHelpfull: Yes(1) No(1)
• See here we have nine places to fit our balls.
  And there are 3 white marbles and 6 black ones.
  So consider for ex there is 1 row and 4 col and given are :
  3 white and 1 black marble.So in this case 1 black marble will take 4 such combinations.
  Hence answer will be 4c3.
  
  So in the same way,
  here there are 9 places and 3 white marbles,remaining black,so ans is 9c3 = 84
• 8 years agoHelpfull: Yes(1) No(0)
• A 3x3 grid have total area = 9.
  No. of ways of arranging 3 white marbles or 6 black marbles is = 9C3 or 9c6 = 84.
• 8 years agoHelpfull: Yes(0) No(0)
• the options are
  a) 8 c 3
  b) ( 9 C 3 + 6 C 3 ) /3!
  c) 9 c 3 + 6 c 3
  d) 6 c 3
  
• 8 years agoHelpfull: Yes(0) No(1)
• I think It's 9c5
• 8 years agoHelpfull: Yes(0) No(3)
• answer should be 9c6
• 8 years agoHelpfull: Yes(0) No(0)
• 84 becoz we have 3 white + black marbel =9total aftr that 4 corners we hve
  so we w'll hve 9c3+9c6=84
• 8 years agoHelpfull: Yes(0) No(1)
• There are total 9 boxes.
  Now, each box can be filled with any of the 9 marbles(3W + 6B). So, there are total 9! ways.
  However, 3 of them are identical and 6 of them are identical so total is 9!/(3!*6!)=84 ways.
• 7 years agoHelpfull: Yes(0) No(1)
• (9c3 * 6c6) + (9c6 * 3c3) = 84+84 = 168 ANSWER
• 6 years agoHelpfull: Yes(0) No(0)