In how many different ways can 300 identical pens can be distributed among all the students of a class of 30 students so that each student gets at least one pen?
Let’s make the question a bit simple. Say we have 6 similar balls and we want to distribute it among 3 persons where each person should get at least one ball.
thnk 6 balls are placed somewhere and we want to divide it into three groups by putting two separators (marks) in between them
This division can be made in many different ways like
Now think what exactly we are doing – we are putting 2 different marks in 5 different places. How many combinations are possible?
Isn’t it 5C2?
Now suppose we did not have the restriction of giving at least one ball to each person.
Then we can put the marks in either end and so total number of places becomes 7 (6 + 2 -1) So its permutation of 7 different items where 2items are of type 1 and 5 are of type 2.
Possible number of arrangements = 7! / 5! 2!
In general,
If n identical objects are to be distributed among m persons then the number of possible ways of doing it is
n-1Cm-1 when each person should get at least one object
Answer is 299C29
w/o the condition (each shd get at least one)the ans ‘ll be 329C29
Can you please explain your answer ???
How you got the numbers!!!
Let’s make the question a bit simple. Say we have 6 similar balls and we want to distribute it among 3 persons where each person should get at least one ball.
thnk 6 balls are placed somewhere and we want to divide it into three groups by putting two separators (marks) in between them
This division can be made in many different ways like
Now think what exactly we are doing – we are putting 2 different marks in 5 different places. How many combinations are possible?
Isn’t it 5C2?
Now suppose we did not have the restriction of giving at least one ball to each person.
Then we can put the marks in either end and so total number of places becomes 7 (6 + 2 -1)
So its permutation of 7 different items where 2items are of type 1 and 5 are of type 2.
Possible number of arrangements = 7! / 5! 2!
In general,
If n identical objects are to be distributed among m persons then the number of possible ways of doing it is
n-1Cm-1 when each person should get at least one object
n+m-1Cm-1 w/o any restriction.
n/a
Hey Nishit, just a question
What if we had 3 red balls and 3 blue balls of same sizes to be distributed among 3 persons?
What would be the approach then? Do reply...
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