M4maths Previous Puzzles

02 Dec 2009 Arrange the balls

There are 6 balls of same size, shape and colour. These balls has to be arranged in 6 boxes of same size,
shape and colour. Total no. of possible methods are

OPtion

1) 8
2) 30
3) 12
4) 36
5) 11
6) 9
7) 144
8) 18
9) 60
10) 72

Solution

Methods are (6,0,0,0,0,0), (5,1,0,0,0,0), (4,2,0,0,0,0), (4,1,1,0,0,0), (3,3,0,0,0,0), (3,2,1,0,0,0), (3,1,1,1,0,0),
(2,2,2,0,0,0), (2,2,1,1,0,0), (2,1,1,1,1,0), (1,1,1,1,1,1)

Correct Option: 5 Best Solution (5)

Dr.Dipin Singh   15 years AGO

(1,1,1,1,1,1)
(2,2,2,0,0,0)
(2,2,1,1,0,0)
(2,1,1,1,1,0)
(3,3,0,0,0,0)
(3,2,1,0,0,0)
(3,1,1,1,0,0)
(4,2,0,0,0,0)
(4,1,1,0,0,0)
(5,1,0,0,0,0)
(6,0,0,0,0,0)
so 11 ways..

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Dimple   15 years AGO

wRITE DIFFERENT POSSIBLE COMBINATIONS.

1 BALL IN EACH BOX..1
2 BALLS IN ONE BOX AND 1 OR 2 BALLS IN OTHER BOXES.... 3 ARRANGEMENTS
.
.
5 BALLS IN ONE BOX .. 1 SET
6 BALLS IN ONE BOX .. 1 SET

LIKE THIS WE GET

1+3+3+2+1+1= 11

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Dolly   15 years AGO

AS BALLS AND BOXES ARE OF SAME TYPE, WE CAN ONLY CONSIDER THE TYPE OF WAYS WE CAN MAKE TOTAL SUM 6 USING MAX 6 PLACES.

SO POSSIBLE COMBINATIONS FROM
000006
TO
111111

THERE ARE 11 COMBINATIONS ONLY.

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Aman   15 years AGO

Check possible arrangements and u will get 11 combinations only as balls and boxes are similar.

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hitesh gakhar   15 years AGO

as all balls and boxes are identical...we have 6 diff cases....

IF ALL GO IN ONE BOX- there's only one possibility,as all boxes are identical...

IF 6 BALLS ARE DISTRIBUTED AMONG 2 BOXES..this has 3 ways...(3-3,2-4,1-5 distribution)

IF 6 BALLS ARE DISTRIBUTED AMONG 3 BOXES..
this has 3 ways....(1-2-3, 2-2-2, 1-1-4 distribution)

IF 6 BALLS ARE DISTRIBUTED AMONG 4 BOXES..
this has 2 ways....(1-1-1-3, 1-1-2-2 distribution)

IF 6 BALLS ARE DISTRIBUTED AMONG 5 BOXES...
this has 1 way...(1-1-1-1-2)

IF 6 BALLS ARE DISTRIBUTED AMONG 6 BOXES...
only one way....(1-1-1-1-1-1)


SO THERE ARE 11 WAYS....

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