Latest TCS Aptitude Question SOLUTION: in how many ways can we distribute 10 identical looking pencil to 4 students so that each student gets at least one pencil? a)5040 b)210 c)84 d)none of these

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(#M40010726) TCS Numerical Ability question Keep an EYE

in how many ways can we distribute 10 identical looking pencil to 4 students so that each student gets at least one pencil?
a)5040
b)210
c)84
d)none of these

Asked In TCS krishnaprasad TATA (11 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

Vivek Ausekar  (11 years ago)

there are 10 pencils
so 1 given to each
hence 6 remains
as per product rule and sum rule
4*(6+5+4+3+2+1)=84

Is this solution Helpfull? Yes (58) | No (12)  

Garima  (11 years ago)

In 84 ways can we distribute 10 identical looking pencil to 4 students so that each student gets at least one pencil.

consider 4 students as A,B,C,D THEN A+B+C+D=10, but each one should get atleast 1 pencil so giving 1 pencil to each student,
the remaining pencils are 10-4=6
now A'+B'+C'+D'=6,
number of non negative integers of A',B',C',D' are (6+4-1)C(4-1)

so total Combinations are 9c3=84,

Is this solution Helpfull? Yes (36) | No (20)  

kunal kumar  (11 years ago)

ans: 84.
we can divide these pencils as:
A B C D total permutation under this division
7 1 1 1 4!/3!=4( divided by 3! becoz 1 is repeted three times)
6 2 1 1 4!/2!=12
5 2 2 1 4!/2!=12
5 3 1 1 4!/2!=12
4 2 2 2 4!/3!=4
4 3 2 1 4!=24
4 4 1 1 4!/(2!*2!)=6
3 3 3 1 4!/3!=4
3 3 2 2 4!/(2!*2!)=6
add all the aboves u will get 84...

Is this solution Helpfull? Yes (22) | No (5)  

aninda  (9 years ago)

ans-number of ways of distributing n identical things among r person where Each person get atleast one things then formula is (n-1)C(r-1).

Is this solution Helpfull? Yes (11) | No (1)  

kalyan pannuru  (11 years ago)

84 is correct please explain it neatly....

Is this solution Helpfull? Yes (7) | No (5)  

Sourabh Malu  (11 years ago)

b)210
10c4=210

Is this solution Helpfull? Yes (5) | No (46)  

drashti nileshkumar desai  (9 years ago)

(n-1)C(r-1)=9C3=84

Is this solution Helpfull? Yes (5) | No (2)  

Abhishek kUNDU  (11 years ago)

@vivek..plz explain your rule.I can't undrstnd..:(
@garima..i think this is right.

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

shyamjee kumar  (11 years ago)

ans a(5040).
for 1st=10ways
for 2nd=9ways
for 3rd=7ways
for 6th=6ways
10*9*8*7=5040 answer

Is this solution Helpfull? Yes (2) | No (45)  

Jyothi Gaduputi  (9 years ago)

n-1cr-1=10-1c4-1=9c3=84

Is this solution Helpfull? Yes (2) | No (1)  

murali  (7 years ago)

give 1 for four students. remaining is 6
6+4-1c4-1=9c3
9c3=84

Is this solution Helpfull? Yes (1) | No   

Devi  (9 years ago)

we have 10 identical pencils,
Task1: distribute 1 pencil each = 1 way ; remaining 6 pencils

Task2: Distribution of 6 identical objects to 4 distinct students is C(6+4-1 , 6)

Is this solution Helpfull? Yes | No (1)  

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