IIT JEE , AIEEE Forum - Mathematics , Algebra - Contest [swordfish #3]: Find ways to distribute identical balls in identical boxes

joyfrancis

I am getting
379 ways

Is it righT?

nunoxic

We Have 30 balls and we have 3 boxes,
now,
ways in which no box is empty
= total ways - ways in which either is empty
= total ways - 3 (any one box is empty)
= 30C3 - 3 (30C2)
= 4060 - 1305
= 2755

spm_nuke

the first box has 28 possibolities the second has 27..

so a net of 28 x 27 = 756 (Ans)

The third boxes number of balls depends on the number of balls in first and second(30-(box1 +box2))

sravanbrahma

the ans should be

30! / (27! * 3!)

b_srikalyan009

i am astound by so many answers i think the below solution is correct.

there are 3 boxes and 30 balls and boxes have atleast 1 ball.

hence fill each box with one ball !

now arrange these 27 balls in 3 boxes this can be done by finding coefficient of

x²⁷ in the expansion of

(x⁰+x¹+x²+............+x²⁷)³ this is called multinomial theorm

=(1-x²⁷)³/(1-x)³

in this expansion u can forget coeff in numerator.

= 29 C 27

=28*29/2

=406

this answer is right

CHANDRASHEKAR SIR is this right????????

punit144

Solve this

raja987654321

As all the balls are identical and each box must have a ball (i.e. none is empty), the problem boils down to C(29,2)= 406

yousuf

Q:find the number of ways to distribute 30 identical balls in to 3 boxes.that no box is remain empty.

30

ANS:30 objects can be put in 3 boxes in 3 ways .and each box remain is empty is in

30

3 -3 ways

ABHI_NARAYANA

this can be done by using combinations.

the balls can be arranged in 30_c3ways and as all balls and boxes are identical there will be no repetetions . so answer is 30c3

-abhilash

nishantsingh89

well let's 30 balls in a row ,
29 places between 30 balls

let's take 2 sticks to be kept in these 29 places, by keeping 2 sticks we divide balls in 3 parts , and we can keep each part in individual boxes

so problem is basically no. of ways of keeping 2 identical sticks in 29 places

the answer is 29C2 = 29*28/2 = 406 ways,

ABHI_NARAYANA

the answer is 30_c3

because all are identical

kishorekumar

the answer is 29C2 = 406

KUSHGEN

priyesh

according to me

all the above are wrong except chandrashekhar sir & aspiredtolive.

the answer is 75

refer to page 4 (soln. by aspiredtolive)

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