How many arrangements of these students on the committee?

[neilparker62]

Homework Statement

Arrange members of committee

Relevant Equations

fundamental counting principle

11.1 10 x 9

11.2.1 10!

11.2.2 I'm not sure.

Attempt at solution:

a) members of same grade must stand together => 5! x 2!
b) Grade 12 in the centre means 1 of 5 groups is fixed but there are 2 ways the centre group can stand => 4! x 2! x2!

 

[PeroK]

ttempt at solution:

a) members of same grade must stand together => 5! x 2!
b) Grade 12 in the centre means 1 of 5 groups is fixed but there are 2 ways the centre group can stand => 4! x 2! x2!

Each of the others grades can stand in two ways as well.

 

[neilparker62]

Each of the others grades can stand in two ways as well.

So with 5 groups of two:

5! x 2^5

and with one of those in a fixed position:

4! x 2^5 ?

 

[PeroK]

So with 5 groups of two:

5! x 2^5

and with one of those in a fixed position:

4! x 2^5 ?

That looks right.