I have a question about permutations

I received a problem in class that I'm having trouble solving.

The problem is:
There are twelve students in the student government (seven seniors and five juniors) who are conducting an election for five officer positions. The positions are senior class president, senior vice president, senior class treasurer, junior class president, and junior vice-president. How many groups of class officers can there be?

I'm not sure how to solve it. Please show work :)

Assuming each senior student can occupy a maximum of one senior post and each junior student can occupy one junior post.

The number of ways of filling the senior posts = n!/(n-k!) = 210
The number of ways of filling the junior posts is n!/(n-k!) = 20

210 * 20 = 4200 ways of filling the posts.

However some of those groups of people will be the same, but with different roles. If you want the number of unique groups then you need combinations not permutations.

The number of ways of filling the senior posts = n!/k!(n-k!) = 35
The number of ways of filling the junior posts is n!/k!(n-k!) = 10

35 * 10 = 350 unique groups of people, whatever roles they fill.

C(7,3) * C(5,2)

as we we have to choose 3 seniors from 7 and 2 juniors from simultaneously.
so on solving it gives 350 i guess.

210 x 20 = 4200 groups

say, a,b,c,d,e,f,g are the seniors and h,i,j,k,l are the juniors....

Permutations without repetition (n=7, r=3)
{a,b,c} {a,b,d} {a,b,e} {a,b,f} {a,b,g} {a,c,b} {a,c,d} {a,c,e} {a,c,f} {a,c,g} {a,d,b} {a,d,c} {a,d,e} {a,d,f} {a,d,g} {a,e,b} {a,e,c} {a,e,d} {a,e,f} {a,e,g} {a,f,b} {a,f,c} {a,f,d} {a,f,e} {a,f,g} {a,g,b} {a,g,c} {a,g,d} {a,g,e} {a,g,f} {b,a,c} {b,a,d} {b,a,e} {b,a,f} {b,a,g} {b,c,a} {b,c,d} {b,c,e} {b,c,f} {b,c,g} {b,d,a} {b,d,c} {b,d,e} {b,d,f} {b,d,g} {b,e,a} {b,e,c} {b,e,d} {b,e,f} {b,e,g} {b,f,a} {b,f,c} {b,f,d} {b,f,e} {b,f,g} {b,g,a} {b,g,c} {b,g,d} {b,g,e} {b,g,f} {c,a,b} {c,a,d} {c,a,e} {c,a,f} {c,a,g} {c,b,a} {c,b,d} {c,b,e} {c,b,f} {c,b,g} {c,d,a} {c,d,b} {c,d,e} {c,d,f} {c,d,g} {c,e,a} {c,e,b} {c,e,d} {c,e,f} {c,e,g} {c,f,a} {c,f,b} {c,f,d} {c,f,e} {c,f,g} {c,g,a} {c,g,b} {c,g,d} {c,g,e} {c,g,f} {d,a,b} {d,a,c} {d,a,e} {d,a,f} {d,a,g} {d,b,a} {d,b,c} {d,b,e} {d,b,f} {d,b,g} {d,c,a} {d,c,b} {d,c,e} {d,c,f} {d,c,g} {d,e,a} {d,e,b} {d,e,c} {d,e,f} {d,e,g} {d,f,a} {d,f,b} {d,f,c} {d,f,e} {d,f,g} {d,g,a} {d,g,b} {d,g,c} {d,g,e} {d,g,f} {e,a,b} {e,a,c} {e,a,d} {e,a,f} {e,a,g} {e,b,a} {e,b,c} {e,b,d} {e,b,f} {e,b,g} {e,c,a} {e,c,b} {e,c,d} {e,c,f} {e,c,g} {e,d,a} {e,d,b} {e,d,c} {e,d,f} {e,d,g} {e,f,a} {e,f,b} {e,f,c} {e,f,d} {e,f,g} {e,g,a} {e,g,b} {e,g,c} {e,g,d} {e,g,f} {f,a,b} {f,a,c} {f,a,d} {f,a,e} {f,a,g} {f,b,a} {f,b,c} {f,b,d} {f,b,e} {f,b,g} {f,c,a} {f,c,b} {f,c,d} {f,c,e} {f,c,g} {f,d,a} {f,d,b} {f,d,c} {f,d,e} {f,d,g} {f,e,a} {f,e,b} {f,e,c} {f,e,d} {f,e,g} {f,g,a} {f,g,b} {f,g,c} {f,g,d} {f,g,e} {g,a,b} {g,a,c} {g,a,d} {g,a,e} {g,a,f} {g,b,a} {g,b,c} {g,b,d} {g,b,e} {g,b,f} {g,c,a} {g,c,b} {g,c,d} {g,c,e} {g,c,f} {g,d,a} {g,d,b} {g,d,c} {g,d,e} {g,d,f} {g,e,a} {g,e,b} {g,e,c} {g,e,d} {g,e,f} {g,f,a} {g,f,b} {g,f,c} {g,f,d} {g,f,e}

Permutations without repetition (n=5, r=2)
{h,i} {h,j} {h,k} {h,l} {i,h} {i,j} {i,k} {i,l} {j,h} {j,i} {j,k} {j,l} {k,h} {k,i} {k,j} {k,l} {l,h} {l,i} {l,j} {l,k}