Compute the number of distinct ways in which 56 toffees can be distributed to 5 persons A,B,C,D and E so that no person receives less than 10 toffees(toffee can not be devided)?

Options : A) 210 B) 240 C) 180 D) 230

Answer is : A

Solution :

Given :-
1. 56 toffees are there
2. 5 members are there
3. no person receives less than 10 toffees

What To Find:- 

No. of distinct ways to distribute.

Procedure :-
1. No person recieves less than 10 toffees.
So distribute 10 toffees to five members.
2. Remaining toffees are 6.
3. These 6 toffees we have got to share for 5 persons.

Formula :- If we share n elements to r members
then number of distinct distributions are : (n+r-1)C(r-1).

4. If we share 6 elements to 5 members.
number of distinct distributions are
(6+5-1)C(5-1) = 10C4 = 210


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