Friday, December 9, 2011

In how many ways 3 identical coins can be placed in 5x5 grid so that no two coin come in same row and same column

First coin can be placed in one of 25 places. For second, only 16 places are possible because of the same column and same row condition. Similarly, only 9 places for third coin. So, total ways = 25 * 16 * 9. but since coins are identical you can't distinguish one from another and thus final answer is ( 25*16*9 ) / 3 = 1200.

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6 comments:

trojan said...

whats the answer ? lol, am getting a huge number...3600 :D

Aashish Barnwal said...

I also got the same answer.
25*16*9
Pls let me know if i am correct.
Thanks
Aashish

Shashank Mani said...

@all actually its not straight farward . u have just choosen possible place where a,b,c can be placed ..but all are not true because question say that no two number can be in same row , column so above asnwer contains common as well so here is i think the correct one

First coin can be placed in one of 25 places. For second, only 16 places are possible because of the same column and same row condition. Similarly, only 9 places for third coin. So, total ways = 25 * 16 * 9. but since coins are identical you can't distinguish one from another and thus final answer is ( 25*16*9 ) / 3 = 1200.

Prabodh said...

I am unable to get how it makes any difference if the coins are identical. In any case, for them to be not-in-line, the number of ways will be 25*16*9

abc123abc said...

I believe it should be 25*16*9/3!
because the coins are identical...

Prabodh said...

You are right...