Latest Elitmus Aptitude Question SOLUTION: Compute the no. of distinct ways in which 56 toffees can be distributed to A,B,C,D,E so that no person receives less than 10 toffees? A)10c6 B)10c5 C)6^3

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(#M40017628) ELITMUS Numerical Ability question Keep an EYE

Compute the no. of distinct ways in which 56 toffees can be distributed to A,B,C,D,E so that no person receives less than 10 toffees?
A)10c6 B)10c5 C)6^3

Asked In Elitmus Akanksha Srivastava (11 years ago)

Solved phani Read Solution (12)

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Read Solution (12) :

krishnesh pathak  (11 years ago)

Distribute 10 toffees to each of 5 persons. so total 50 toffees , now remaining toffees are 6 which we hav to distribute among 5 person so this can be possible in
6+5-1C5-1=10C4=10C6 so option will be A

Is this solution Helpfull? Yes (68) | No (5)  

phani  (11 years ago)

distribute 10 toffes to each first: after that 6 toffes (r),5 persons(n)
(n+r-1)C(r-1)=10C5

Is this solution Helpfull? Yes (25) | No (32)  

gourav bibhor  (9 years ago)

NO PERSON RECEIVES LESS THAN 10 TOFFEES
so 50 toffees are distributed equally i.e 10 toffees to each of A,B,C,D,E
now (56-50=6) toffees are to be distributed among 5 persons

we know that
number of ways in which n identical things can be distributed among r persons, each one of them can get 0,1,2 or more
=(n+r-1)C(r-1)

here n=6(toffee) is to distributed among r=5(persons)

no. of ways=(6+5-1)C(5-1)=10C4=10C6

Is this solution Helpfull? Yes (17) | No   

shakti prakash mishra  (11 years ago)

@akanksha...
this question was asked in elitmus...??

Is this solution Helpfull? Yes (15) | No (8)  

NESAB JAFAR  (9 years ago)

(a+10)+(b+10)+(c+10)+(d+10)+(e+10)=56(all of them will receive atleast 10 toffee)
a+b+c+d+e=6 (we distribyted 6 among 5 )total no. of ways 10c4=10c6

Is this solution Helpfull? Yes (2) | No   

arun kumar  (8 years ago)

distribute 10 coffee to each so total 50 toffees,and now remaining toffee are 6 and now we have to distribute 6 toffee in 5 person.let n=6,r=5 so total way is (n+r-1)C(r-1)=(6+5-1)C(5-1)
=10C4.
why i used this formula you can understand from this explanation.
Consider that the number of identical objects as n.Now consider that all the n objects are placed on a row.Let us assume some separators that separates the n objects.Now as we want to separate them into r group[as blank groups are also allowed],take the separators as objects.Now we need r-1 separators to make r groups.Therefore total number of objects is n+r-1.There will be r-1 places for the separators to occupy.Therefore we can arrange the separators in
(n+r-1)C(r-1) ways, which is the answer to the question asked.

Is this solution Helpfull? Yes (2) | No   

Deepak Kumar  (9 years ago)

first we will distribute 10 toffees to each of 5 persons i.e total 50 toffees ,
now remaining toffees are 6 which we have to distribute among 5 person so this can be possible in
m+r-1 C r-1
=>6+5-1C5-1=10C4

Is this solution Helpfull? Yes (1) | No   

virender kumar  (6 years ago)

option 4 is 5^6
the ans is 5^6

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

maharaja  (9 years ago)

samjh nahi aaya...bhai solution...

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kaustubh salunke  (9 years ago)

option a.is the ans

Is this solution Helpfull? Yes | No   

Govind Singh  (8 years ago)

NO PERSON RECEIVES LESS THAN 10 TOFFEES
so 50 toffees are distributed equally i.e 10 toffees to each of A,B,C,D,E
now (56-50=6) toffees are to be distributed among 5 persons

we know that
number of ways in which n identical things can be distributed among r persons, each one of them can get 0,1,2 or more
=(n+r-1)C(r-1)

here n=6(toffee) is to distributed among r=5(persons)

no. of ways=(6+5-1)C(5-1)=10C4=10C6
Read more at http://www.m4maths.com/17628-Compute-the-no-of-distinct-ways-in-which-56-toffees-can-be-distributed-to-A-B-C-D-E-so.html#3GwjU8Y8ft7ZtyiF.99

Is this solution Helpfull? Yes | No (4)  

RAJ  (7 years ago)

a,b,c,d,e>10
let us assume k>=1
now a,b,c,d,e,k>=11
So 11-1C6-1=10C5

Is this solution Helpfull? Yes | No (3)  

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