Da Shari wants to rearrange the four sweaters, two coats, and five jackets that are in her closet. If she puts a sweater first and a jacket last, how many different ways can she arrange them?

Solution:

Fabric possessed by Da. Shari = 4 Sweaters + 2 Coats + 5 Jackets = 11 in all

Arrangement that Da Shari wants to arrange 4 Sweaters + 2 Coats + 5 Jackets is to put "a sweater first and a jacket last".

After putting a sweater first and jacket last, total fabric which needs to be arranged is (3 Sweaters + 2 Coats + 4 Jackets) = 9 in all.

Total number of possible arrangement = (1 sweater) * [9 fabric = (3 Sweaters + 2 Coats + 4 Jackets) arrangement] * (1 Jackets)

= 1! * 9! * 1!

= 9!

= 9 * 8 * 7 * 6 * 5 * 4 * 3*2*1

= 362,880 ways