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805+ (Hard)|   Combinations|      
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You are given a 4×4 square Board and you need to fill it with Red and 07 Mar 2020, 02:33
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95% (hard)

Question Stats:

19% (03:17) correct 81% (02:16) wrong based on 57 sessions

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You are given a 4×4 square Board and you need to fill it with Red and Blue colors such that there are exactly two blue boxes and two red boxes in each row and column. In how many ways is it possible to fill the colors in 4×4 square Board.

A. 12
B. 45
C. 48
D. 90
E. 96
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D
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You are given a 4×4 square Board and you need to fill it with Red and 08 Mar 2020, 05:42
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nick1816
You are given a 4×4 square Board and you need to fill it with Red and Blue colors such that there are exactly two blue boxes and two red boxes in each row and column. In how many ways is it possible to fill the colors in 4×4 square Board.

A. 12
B. 45
C. 48
D. 90
E. 96
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Can you send it's solution?

Posted from my mobile device
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You are given a 4×4 square Board and you need to fill it with Red and Updated on: 09 Mar 2020, 01:54
Originally posted by nick1816 on 08 Mar 2020, 10:58.
Last edited by nick1816 on 09 Mar 2020, 01:54, edited 1 time in total.
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the first row can be arranged in number of ways= 4C2= 6

after first step...first column can be arranged in = 3C2 ways = 3

It's obvious upto now....What's interesting is to arrange rest 3 by 3 matrix.

it's (1+2*2). (try to find it)

Total number of ways= 6*3*5= 90





yashikaaggarwal
nick1816
You are given a 4×4 square Board and you need to fill it with Red and Blue colors such that there are exactly two blue boxes and two red boxes in each row and column. In how many ways is it possible to fill the colors in 4×4 square Board.

A. 12
B. 45
C. 48
D. 90
E. 96

Can you send it's solution?

Posted from my mobile device
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You are given a 4×4 square Board and you need to fill it with Red and 08 Mar 2020, 19:37
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nick1816
the first row can be arranged in number of ways= 4C2= 6

after first step...first column can be arranged in = 3C2 ways = 3

It's obvious upto now....What's interesting is to arrange rest 3 by 3 matrix.

it's (1+2C2+2C2). (try to find it)

Total number of ways= 6*3*5= 90





yashikaaggarwal
nick1816
You are given a 4×4 square Board and you need to fill it with Red and Blue colors such that there are exactly two blue boxes and two red boxes in each row and column. In how many ways is it possible to fill the colors in 4×4 square Board.

A. 12
B. 45
C. 48
D. 90
E. 96

Can you send it's solution?

Posted from my mobile device
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nick1816

it's (1+2C2+2C2). (try to find it)

Please elaborate
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You are given a 4×4 square Board and you need to fill it with Red and 09 Mar 2020, 23:20
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Selected 90 based on a guess.
Knew it had to be less that 4!*4 = 96 and more that 4C2*4C2*2C2*2C2*2 = 72

90 is the only one that fits this.

Curious what the actual solution methodology is.
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You are given a 4×4 square Board and you need to fill it with Red and 10 Mar 2020, 00:32
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took educated guess but still took 1 minute 52 second to get 90 .
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You are given a 4×4 square Board and you need to fill it with Red and 10 Mar 2020, 01:37
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Kinshook

I made a typo earlier. It's 2C1.

No. of ways to fill second row is 3C2

​
Now from these 3 ways,

- - One will lead to complete filled board [ when the colours in first row and second row match ] { 1× 1 }

( because there can be only 2 blocks of same colour in a line )

- - Other two will lead to two cases each [ as on filling the opposite colours, we would go to the leftmost empty block of 3rd row. There we will have 2 colours to fill in, so 2 ways ] { 2C1+2C1 }
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You are given a 4×4 square Board and you need to fill it with Red and 22 Feb 2025, 10:45
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