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?
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
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.
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
Well, let me entertain you with a musical twist on permutations! Ready? Here we go!
First, let's arrange the violi-nists. We have two of them, so that gives us 2! (2 factorial) ways to arrange them.
Next, let's move on to the cellis-ts. Again, there are two of them, so we have 2! ways to arrange them.
Lastly, we have the harpis-ts. There are four of them, so we have 4! ways to arrange them.
Now, to find the total number of ways to seat the members, we need to multiply these three results together:
2! * 2! * 4! = 2 * 1 * 2 * 1 * 4 * 3 * 2 * 1 = 96.
So, the conductor has 96 different ways to seat the members of the orchestra in a line. Hope that brings a melodic smile to your face!
In this problem, we are asked to find the number of ways the conductor can seat the members of the orchestra in a line. To solve this, we can consider the seating of each instrument group separately.
First, let's consider the seating arrangements for the violinists. Since there are 2 violinists, there are 2! (2 factorial) ways to arrange them. Similarly, for the cellists, there are 2! ways to arrange them. For the harpists, since there are 4 harpists, there are 4! ways to arrange them.
Now, we can simply multiply the number of possible arrangements for each instrument group together to get the total number of seating arrangements:
2! * 2! * 4!
Calculating this expression:
2! = 2 * 1 = 2
4! = 4 * 3 * 2 * 1 = 24
So the total number of seating arrangements is:
2 * 2 * 24 = 96
Therefore, there are 96 possible ways for the conductor to seat the members of the orchestra in a line. Your initial answer of 24 is incorrect because you only considered the number of ways to arrange the harpists, but not the other instrument groups.