Question

A choir of singer is made up of 7 soprano,5alto,5tenor and 6 bass singer.In a performance,the choir will stand in two rows.In how many ways can the singer be arranged
a)if there are no restriction
b)if sopranos and altos must be in the front row while the rest in the back row
c)if condition in (b) applies,and each type of voice must be grouped together
can someone help me on this?pleaaaseee

Answer 1

for a) do they have to be in groups??

Answer 2

i think no

Answer 3

23C0*23!+(23C1*22!*1!)+(23C2*21!*2!) ... all the way up to 23
I guess, I am not sure at all.

Answer 4

how to do this?i was wondering,how to arrange in two rows without knowing how many people in one row?can you explain about your solution?

Answer 5

23C0*23! --> all people are in same row -> 0 on one row
we can arrange 23 people in 23! ways

Answer 6

in second term, we select 1 person, that can be done in 23C1 ways, and arrange 22 people in 22! ways.

Answer 7

and so on?how about question b?

Answer 8

is a) correct ??

Answer 9

11C0*12!*11!+11C1*13!*10!+11C2*13!*10!+ all the way up to 11

Answer 10

this is also a guess.