Problem Solving

If 16 oranges are distributed among 4 children such that each gets at least 3 oranges, the number of ways of distributing them is

A) 30
B) 210
C) 15
D) 35
E) 40

I don't have the OA for this.

Following can be the only possible combinations:

(3337), (3346), (3355), (3445) and (4444)
So total number of ways of distributed (3337) among 4 is = 4

Number of ways of distributing (3346) is = 12

Number of ways of distributing (3355) is = 6

Number of ways of distributing (3445) is = 12

Number of ways of distributing (4444) is = 1

So total is 4+12+6+12+1 = 35

D

beat_gmat_09 wrote:If 16 oranges are distributed among 4 children such that each gets at least 3 oranges, the number of ways of distributing them is

A) 30
B) 210
C) 15
D) 35
E) 40

I don't have the OA for this.

sachin2411 wrote:Following can be the only possible combinations:

(3337), (3346), (3355), (3445) and (4444)
So total number of ways of distributed (3337) among 4 is = 4

Number of ways of distributing (3346) is = 12

Number of ways of distributing (3355) is = 6

Number of ways of distributing (3445) is = 12

Number of ways of distributing (4444) is = 1

So total is 4+12+6+12+1 = 35

D

Even I am getting 35-
Assume that 3 oranges are distributed among 4, total distributed = 3*4 = 12
Left = 16-12 = 4 oranges.
To distribute 4 oranges among 4 children use this relation - C(n+r-1,n-1)
n=r=4
C(4+4-1,4-1) = C(7,3) = 35

Yes its more concise i guess, but people should know the non negative integral solution of a+b+c+d=4, if you know then you are done.

beat_gmat_09 wrote:

sachin2411 wrote:Following can be the only possible combinations:

(3337), (3346), (3355), (3445) and (4444)
So total number of ways of distributed (3337) among 4 is = 4

Number of ways of distributing (3346) is = 12

Number of ways of distributing (3355) is = 6

Number of ways of distributing (3445) is = 12

Number of ways of distributing (4444) is = 1

So total is 4+12+6+12+1 = 35

D

Even I am getting 35-
Assume that 3 oranges are distributed among 4, total distributed = 3*4 = 12
Left = 16-12 = 4 oranges.
To distribute 4 oranges among 4 children use this relation - C(n+r-1,n-1)
n=r=4
C(4+4-1,4-1) = C(7,3) = 35