Posted by Shreya on .
permuations
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?

Pre Calculus 12 
Reiny,
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 
Pre Calculus 12 
Shreya,
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 
Pre Calculus 12 
Steve,
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.