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?