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eriks7779
07.04.2020 •
Mathematics
In how many ways can $3$ identical red balls, $3$ identical green balls, and $3$ identical blue balls be arranged in a $3\times 3$ grid, such that each row and each column of the grid contains $1$ ball of each color
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Ответ:
Step-by-step explanation:
GIVEN:
identical red balls,
identical green balls, and
identical blue balls be arranged in a
grid.
TO FIND: In how many ways can balls be arranged such that each row and each column contains
ball of each color.
SOLUTION:
As each column and row must contain a red,a green and a blue ball.
Consider the image attached
each column contains a green,a blue and a red ball
To find more number of ways of arrangement, columns can be arranged differently such that each row will still contain each of three ball.
Now,
Total number of ways of arranging
columns ![=3!](/tpl/images/0586/8400/abad3.png)
Hence total number of ways such that each row and each column of the grid contains
ball of each color is ![6](/tpl/images/0586/8400/5ae83.png)
Ответ:
then stop asking questions...?
Step-by-step explanation: