A choir consists of 13 sapranos,12 altos,6 tenors, and 7 basses.A group consisting of 10 sapranos, 9 altos, 4 tenors and 7 basses is to be chosen from the choir.

Question

Q.The 4 tenors and 4 basses stand in a single line with all the tenors next to each other and all the basses next to each other.How many possible arrangement are there if 3 of the tenors refuse to stand next to any of the basses?

Answer 1

there are 13C10 ways to pick the 10 sopranos
and so on for the other voices.
Now just multiply all those combinations together.

There is only 1 tenor who will stand next to the basses.
There are 3! ways to arrange the oher tenors, and 4! ways to arrange the basses.
Then there are two ways to arrange the sections: Tenors-basses and basses-tenors.
So, 2*3!*4! ways in all.