Latest self Aptitude Question SOLUTION: in how many ways can we distribute 10 identical looking pencils to 4 students so that each student gets at least 1 pencil?

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(#M40011177) SELF Logical Reasoning question Keep an EYE

in how many ways can we distribute 10 identical looking pencils to 4 students so that each student gets at least 1 pencil?

debopama sarkar (11 years ago)

Unsolved Read Solution (8)

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giri  (11 years ago)

first we distribute 4 pencils each 1 to 4 students. remaining pencils are 6. then ways of distributions are (n+r-1)C(r-1) here n=6 & r=4
hence 9C3=84

Is this solution Helpfull? Yes (146) | No (12)  

praneeth  (10 years ago)

first we shall distribute 4 pencils to each student.now we have 6 pencils remaining.using stars and bars formula we get(6+4-1)c(4-1)=9c3=84

Is this solution Helpfull? Yes (36) | No   

ANGEL ISRANI  (10 years ago)

please explain properly.
how we got n+r+1 c r-1

Is this solution Helpfull? Yes (14) | No (8)  

kiran ks  (11 years ago)

ANS:210
out of 10 4 is distributed to students, so 6 is remaining
now, we will distribute remaining 6 pencils to 10 students in 10C6 ways
=10C4= (10*9*8*7)/(4*3*2*1)=210

Is this solution Helpfull? Yes (9) | No (153)  

NAGIRI SRINIVASARAO  (6 years ago)

To get each student gets at least 1 pencil.First, we distribute 4 pencils each 1 to 4 students.
Remaining pencils are 6(Total 10 pencils we already distribute 4 pencils).
Number of ways of distributing n identical things among r persons when each person may get any
number of things =(n+r-1)C(r-1)
here n=6 & r=4
hence 9C3=84
Therefore answer is 84 ways.

Is this solution Helpfull? Yes (6) | No   

divya  (8 years ago)

Since the pencils are identical, we can just give one to each student leaving six to be given out. The number of ways to distribute n identical objects among r people is given by (n+r−1)c(r−1). For our problem, this is (93)=84.

Is this solution Helpfull? Yes (3) | No (1)  

gomathi  (9 years ago)

posibility of 10 pencils to 4 persons is 10c4 is 210

Is this solution Helpfull? Yes | No (20)  

Vinoth  (8 years ago)

1st each needs 1
So 10C4 = 210
2nd 6 to 4 students including 0
What is the number of ways in which n identical objects can be divided into r groups where each group can have any number of objects including 0?
The formula is (n+r-1) C (r-1)
This is called the Bose-Einstein coefficient

(6+4-1)c(4-1)=9c3=84
210 x 84 =17640

Is this solution Helpfull? Yes | No (13)  

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