Hey! We 've verified this expert answer for you, click below to unlock the details :)
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.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
In how many different ways can we put all 5 identical balls in a 3\(\times\)3 grid .
Such that each row contains was atleast one ball.
Not the answer you are looking for? Search for more explanations.
no mod power today sorry ;~;
think about choosing 4 blanks squares from 9, maybe
answer is 108
There are 9 C 5 = 126 ways to place the balls without worrying about whether all rows have at least one ball or not.
If we focus on the cases where one row is left out, like row 3 left out, then we have 6 C 5 = 6 ways to fill up the first two rows only. So there are 3*6 = 18 ways to fill up 2 rows only leaving out one row blank
The last thing to do is subtract
126 - 18 = 108
how is leaving one row empty and chossing 5 out 6 and multiplying by 3
is similar to condition at least one row has one ball
Well you only have 2 options: you either have each row have at least 1 ball OR one row gets left out entirely
when I calculated the "18", that's the number of ways to leave out 1 row
I subtracted from 126 because of this property
(number of ways where each row gets at least 1 ball) + (number of ways to leave out one row entirely) = total number of ways to fill up the slots