In how many ways can one write the numbers 1, 2, 3, 4, 5, and 6 in a row so that given any number in the row, all of its divisors (not including itself) appear to its left?
plz help i am stuck
I wrote a computer program:
For a = permutation[1,2,3,4,5,6]
good = 1;
if i > j and a[j] % a[i] = 0 then good = 0;
count = count + good
write(output,count);
output = 7.
1,2,3,4,5,6
1 has to go first.
1, 23456
2,3, and 5 are prime so they can go in any order in relation to one another.
4 has to go after 2
6 has to go after both 2 and 3
Each time there are 5 spots for the 5
1,2,3,4,6 5ways with the 5 included
1,2,3,6,4 5ways with the 5 included
1,2,4,3,6 5ways with the 5 included
1,3,2,4,6 5ways with the 5 included
1,3,2,6,4 5ways with the 5 included
So I get 25 ways.