Question

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 diferent ways can she arrange them?

Answer 1

Answer: There is 362880 ways she can arrange them.

Explanation:

Since we have given that

Number of sweaters she has = 4

Number of coats she has = 2

Number of jackets she has = 5

According to question, we have asked to put sweater first, and a jacket last,

So, remaining items will be

`11-(1+1)\\\\=11-2\\\\=9`

So, we will use "Fundamental Theorem of Counting " as arrangement is needed:

So, it becomes,

`1* 9!* 1\\\\=9* 8* 7* 6* 5* 4* 3* 2* 1\\\\ =362880\ ways`

Hence, there is 362880 ways she can arrange them.