#self doubt

Question

Can someone please explain the following case of combination

I means identical

D means different 

DOIB with boxes being empty and non empty

As in this question the given value in question itself i am not able to interpret.

https://gateoverflow.in/420251/go-classes-test-series-2024-mock-gate-test-12-question-17

 

Answer 1

In that question, we have 10 distinguishable objects and 3 indistinguishable piles and one condition was also there that all piles should be non-empty.

Since we have indistinguishable piles so only numbers of objects matter not order e.g. 1,1,8 and 8,1,1 are the same thing.

A	B	C	Calculation	total
1	1	8	(C(10,8) * C(2,1) *C(1,1))/2	45
1	2	7	(C(10,7) * C(3,2) *C(1,1))	360
1	3	6	(C(10,6) * C(4,3) *C(1,1))	840
1	4	5	(C(10,5) * C(5,4) *C(1,1))	1260
2	3	5	(C(10,5) * C(5,3) *C(2,2))	2520
2	2	6	(C(10,6) * C(4,2) *C(2,2))/2	630
2	4	4	(C(10,4) * C(6,4) *C(2,2))/2	1575
3	3	4	(C(10,4) * C(6,3) *C(3,3))/2	2100
			TOTAL ----->	9330

(A,B,C are indistinguishable only just name them for simplicity).