Latest Elitmus Aptitude Question SOLUTION: 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

• Placement Papers
• /
• Elitmus
• /
• Numerical Ability
• /
• Permutation and Combination

Elitmus Question Papers:

(#M40155977) ELITMUS Numerical Ability question Keep an EYE

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

Asked In Elitmus insha singh (8 years ago)

Unsolved Read Solution (14)

Is this Puzzle helpful?   (7)   (3) Submit Your Solution Permutation and Combination

Read Solution (14) :

Subha Mahapatra  (8 years ago)

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

Is this solution Helpfull? Yes (17) | No   

richa gargi  (8 years ago)

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

Is this solution Helpfull? Yes (8) | No (4)  

Suman Das  (8 years ago)

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

Is this solution Helpfull? Yes (7) | No   

suraj kumar  (8 years ago)

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

Is this solution Helpfull? Yes (3) | No   

gopi reddy  (8 years ago)

The answer is 9 c 3 or 9 c 6. i.e 9 c 3 + 9 c 6.

Is this solution Helpfull? Yes (2) | No (4)  

Subha Mahapatra  (8 years ago)

Option A should be 9c3 not 8c3 because the answer is 9c3.

Is this solution Helpfull? Yes (1) | No (1)  

sulabha naware  (8 years ago)

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

Is this solution Helpfull? Yes (1) | No   

Subha Mahapatra  (8 years ago)

A 3x3 grid have total area = 9.
No. of ways of arranging 3 white marbles or 6 black marbles is = 9C3 or 9c6 = 84.

Is this solution Helpfull? Yes | No   

insha singh  (8 years ago)

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

Is this solution Helpfull? Yes | No (1)  

Dilli P H  (8 years ago)

I think It's 9c5

Is this solution Helpfull? Yes | No (3)  

SHALINI SINGH  (8 years ago)

answer should be 9c6

Is this solution Helpfull? Yes | No   

juhi  (8 years ago)

84 becoz we have 3 white + black marbel =9total aftr that 4 corners we hve
so we w'll hve 9c3+9c6=84

Is this solution Helpfull? Yes | No (1)  

Yogesh  (7 years ago)

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.

Is this solution Helpfull? Yes | No (1)  

jyoti shankar  (6 years ago)

(9c3 * 6c6) + (9c6 * 3c3) = 84+84 = 168 ANSWER

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.