permuations

Question

an orchestra has 2 violinsts, 2 cellisst, and 4 harpists. Assume that the players of each instrument have to sit together, but they can sit in their own group. In how many ways can the conductor seat the members of the orchestra in a line?

I just went 4*3*2 and got 24? is that wrong?

Answer 1

visualize the groups V,C,H
these groups can be arranged in 3! ways or 6 ways

but within each group, the
violinists can be arranged in 2 way
the cellists in 2 ways
the harpists in 4! or 24 ways

so the number of arrangements
= 6(2x2x24) or 576 ways

Answer 2

Oh but this is a multiple choice question and the only answers that it can be are

A 144
B 72
C 24
D 1728

Answer 3

It looks to me like you have a typo somewhere. Your answer of 4*3*2 indicates that there were 3 violinists or 3 harpists. In that case, multiply Reiny's answer by 3 to get 1728.