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

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it