Binary combination/permutation help

Hello helpful smart community :)

i have some questions involving permutation/combinations and need your help.

here it goes:

im tring to find out how many different arrangements of 4 (1's) can be put in 40 (0's)

ex:

: 0000000000000000000000000000000000000000 empty

1 : 1111000000000000000000000000000000000000

2 : 0000000000000000000000000000000000001111

3 : 0000010001000000000000001000000000000100

etc....

how do i calculate that? O.o

also what is the chance of finding specific one of those in 1000000 random attempts.

any idea's?

Re: Binary combination/permutation help

Your task can be rephrased to distributing 35 objects into 5 buckets.

Re: Binary combination/permutation help

hmmmm thanks for reply but im getting the feeling thats not it ^^

can you explain more please?

i think i found out how to do it, but can someone explain to me how to calculate it exactly?

Math Forum - Ask Dr. Math

Re: Binary combination/permutation help

Yours is the "Empty Urns are Allowed" case.

Re: Binary combination/permutation help

Hellom, zipzaaaap6656!

Quote:

(a) How many different arrangements are there for four 1's and forty 0's?

We have a 44-digit number.

The four 1's can be placed in . ways.

The forty 0's are placed in the remaining positions.

Therefore, there are 135,751 possible arrangements.

Quote:

(b) What is the probability of finding a specific number in 1,000,000 random attempts.?

I'll assume that the selection is made *with* replacement.

. . . . . .