i have 2 permutation questions

1. how many words consisitng of 3 vowel and 2 consonants can be formed from the letters of the word "columbians"

2. a presidnet secretry and treasurer are to be named from 5 men and 3 women

how many permutations are there if one man and one women must be picked

heres how much i have done

1) you have 4 vowels and 6 consonants and 10 letters total

you need a 5 letter permutation

so you have 4 x 3 x 2 x 6 x 5

but if you do this, will you always have the order in 3 vowels and 2 consonants? what do i multiply this by to mix it up?

keep in mind my total permutations without limits is 10!/5!

2) so i do the same thing as above, i know 5 men, 3 women and a total of 8 ppl

5 x 3 x 6

but wont the man always be president? again, how do i mix this up??

sorry if my english not very good