Homework Help: Pre Calculus 12

Posted by Shreya on Friday, January 25, 2013 at 12:43am.

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, Friday, January 25, 2013 at 10:41am
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, Friday, January 25, 2013 at 11:26am
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, Friday, January 25, 2013 at 11:30am
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.

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