Find the number of ways you can fill a 3x3 grid (with 4 corners defined as a,b,c,d) if you have 3 white marbles and 6 black marbles

A. 9 C 3

B. 6 C 3

C. 9 C 3 + 6 C 3

D. (9 C 3) + (6 C 3)/3!

• we have to arrange 9(3 white+6 black) marbles in 9 places of 3x3 grid.
  i.e we can arrange in 9! ways as 3 white and 6 black marbles are there
  total number of ways will be
  9!/(3!*6!) ways = 9 c 3
• 10 years agoHelpfull: Yes(3) 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. A) 9C3
• 10 years agoHelpfull: Yes(1) No(0)