Each of 8 identical balls is to be placed in the squares shown in the figure given in a horizontal direction such that one horizontal row contains 6 balls and the other horizontal row contains 2 balls .In how many different ways can this be done

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

Each of 8 identical balls is to be placed in the squares shown in the figure given in a horizontal direction such that one horizontal row contains 6 balls and the other horizontal row contains 2 balls .In how many different ways can this be done

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

1 Attachment
i am dizzy already
how many squares how many parallelograms

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

|dw:1441070677769:dw|
\(\large \color{black}{\begin{align} & \normalsize \text{Each of 8 identical balls is to be placed in the squares shown} \hspace{.33em}\\~\\ & \normalsize \text{ in the figure given in a horizontal direction such that one } \hspace{.33em}\\~\\ & \normalsize \text{horizontal row contains 6 balls and the other horizontal row} \hspace{.33em}\\~\\ & \normalsize \text{ contains 2 balls .In how many different ways can this be done} \hspace{.33em}\\~\\ & a.)\ 38 \hspace{.33em}\\~\\ & a.)\ 28 \hspace{.33em}\\~\\ & a.)\ 16 \hspace{.33em}\\~\\ & a.)\ 14 \hspace{.33em}\\~\\ \end{align}}\)
none of the above
so for 1 complete horizontal row filled we have 6Choose 2 + 4so 2* (6 choose 2 + 4) for the complete case?
38
|dw:1441071022533:dw|
|dw:1441070953833:dw|
im not sure if that is possible because then the 6 are vertical
that why in the beginning they were like oh its horizontal given this picture as it is
dan's \(\large \dbinom{2}{1}*(4+\dbinom{6}{2})\) looks neat to me!
plus if it is vertical u can no longer have a case where the remaining 2 can be a pair of horizontal theyd have to be tripple or 2 pairs of horizontal
keeping ball B still at that position and moving ball A anywhere between 1-6x6 we get 6 cases ball B can go anywhere between its original postion -13 so we get 6x4 cases =24 ball B can also be put at any position 1-6 with ball A so get -6x5 more cases =30 so the answer =24+30=54
With horizontal only, I also have \(\Large 2*\dbinom{6}{6}*(\dbinom{6}{2}+4\dbinom{2}{2})=38\)
did i do something wrong?
``` keeping ball B still at that position and moving ball A anywhere between 1-6x6 we get 6 cases ball B can go anywhere between its original postion -13 so we get 6x4 cases =24 ``` Nice idea, but there are some duplicates, double check
the duplicates are because of counting AB and BA as two different things but the balls are identical, so AB and BA must be counted only once |dw:1441071598536:dw|
``` keeping ball B still at that position and moving ball A anywhere between 1-6x6 we get 6 cases ball B can go anywhere between its original postion -13 so we get 6x4 cases =24 ball B can also be put at any position 1-6 with ball A so get -6x5 more cases =30 ``` simply divide that by 2 to fix that duplicates issue
@dan815 Have you worked out the number of rectangles yet? lol
haha xD
|dw:1441072190782:dw|
in this case where i m moving ball A only in 1-6 we r getting 13x6 cases woah its even more nd we can assume the question to be this - find the number of possible combinations ...keeping 6 balls in a row with 2 balls free to move its ok to no to consider that 2balls kept in horizontal cause that will happen in each and every case
no there are only 8 balls you must put 2 balls horizontal in one row and 6 balls horizontal in another row
I said 64 because 8 goes into 6 = 48 time and 8 goes into 2 = 16 time then i added them together and got 64
hey since the asker is gone i thought wed go over htis problem too, so how many rectangles/squares are there in that figure
|dw:1441072848851:dw|
i tried 2*(3choose 2 * 7 choose 2) - (3 choose 2)^2
29 squares easy to count one by one :)
|dw:1441072894766:dw|
thanks @ganeshie8 :D
` 2*(3choose 2 * 7 choose 2) - (3 choose 2)^2` looks good to me basically you need 2 horizontal lines and 2 vertical lines to form a rectangle
right thats what i was thinking
right im just translating ur math symbols to layman english
Here is a more complicated but fun problem find the order of the group of symmetries of given pattern
o boy
like the number of every unique rectangle?
a group is a set with a binary operation that is associative, has an identity element and inverses exist for each element
here the group is the set of all symmetries of given pattern operation is "composition"
by "set of all symmetries" i mean all the transformations that bring the pattern back to itself for example, rotating the pattern by 90 degrees wont change it so \(R_{90}\) is a group element
similarly a horizontal flip wont change the pattern so "horizontal flip" is also a group element i think it is an easy problem, its just the terminology that gets in the way..
i didn't understand this \(\large \dbinom{2}{1}\times \left(4+\dbinom{6}{2}\right)\)
teamviewer ?
wait
sry no teamviewer , m on mobile connection
2 rows
its okay so we are doing the problem in two steps : 1) choose a row, then choose 6 squares in that row for placing 6 balls 2) after that, choose another row and 2 squares in that row for placing 2 balls
look at the given pattern how many rows have at least 6 squares ?
2 rows ?
1) `choose a row`, then choose 6 squares in that row for placing 6 balls yes, you can choose \(1\) row from the available \(2\) rows in \(\dbinom{2}{1}\) ways
1) choose a row, then `choose 6 squares in that row for placing 6 balls` then you can choose 6 squares in that row in \(\dbinom{6}{6}\) ways so step1 can be done in \(\dbinom{2}{1}*\dbinom{6}{6}\) ways
ok
let me know once you digest step1
i digested
|dw:1441074443487:dw|
after step1, situation might look something like above
lets see step2
yes
2) after that, `choose another row` and 2 squares in that row for placing 2 balls here we need to be careful because not all rows have same number of squares
2*6C2+4*2C2
|dw:1441074636585:dw|