Find the number of ways you can fill a 3*3 grid ( wit h4 corners defined as a,b,c,d) if you have 3 white marbles and 6 black marbles

a.9c3
b.6c3
c.9c3+6c3
d.9c3+6c3/3!

Approach please...????

• ans: 9c3
  we can choose any 3 places for white marbles in 9c3 and remaining places are left for black marbles;
  we do not hve to arrange them because they all are identical
• 7 years agoHelpfull: Yes(12) No(1)
• 3*3=9
  No of ways we can select 3 white marbles out of total 9 marbles=9c3
  Remaining marbles left=9-3=6
  No of ways we can select 6 black marbles of the remaining 6 marbles=6c6
  So, total ways of arranging=9c3*6c6 i.e 9c3*1
  Therefore, Ans=9c3
• 7 years agoHelpfull: Yes(6) 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
• 7 years agoHelpfull: Yes(3) No(1)
• There are 9 places to be filled. But Since the balls are identical, so we have to arrange 9 balls in 9 places. This gives us 9! but the balls are identical so you have to divide the identical numbers factorial from it. so the final answer is 9!/(3!*6!) which is equal to the 9C3.
• 7 years agoHelpfull: Yes(1) No(0)
• 3X3 grid mean 9 place to occupy. and we got 3+6= marbles
  
  so,
  
  9!/3!*6! {3! for 3 similar white marbles and 6! for similar black marbles.
  
  and the above ans is equal to 9C3
• 7 years agoHelpfull: Yes(0) No(1)
• The answer will be 9c3. Because there are 9 places in which we can place those tiles, suppose we assume them in a row-wise manner. so we can fill them w w w b b b b b b. So we can arrange them 9! ways but there are 3 w(white) and 6 b(black) tiles which are not identical. So we have to divide 9! by 3!*6!. So the final answer will be 9!/(3!*6!) which is same as 9c3.
• 7 years agoHelpfull: Yes(0) No(1)
• option a
  9!/(3!*6!)=9c3
• 7 years agoHelpfull: Yes(0) No(0)