Word problem

Question

Jenny has nine different skirts seven different tops ten different pairs of shoes two different necklaces and five different bracelets in how many ways can Jenny dress up

Answer 1

Let's start with what the question tells us...

- Jenny has 5 different types of things to wear 9 skirts, 7 tops, 10 pair of shoes, 2 necklaces, and 5 bracelets

Now what is the question asking...

- How many ways can she combine these items (we will assume she wants to wear on and only one of each kind and that everything matches:)

 

She walks into her closet and grabs a skirt, one of a possible 9.  Then she grabs a top, one of a possible 7.  With the first skirt she can make a possible 7 different combinations of skirt and top.  If she chooses a different skirt she can make 7 more combinations.  This can keep going until she has used each skirt creating 9 sets of 7 or 9 x 7=63

 

She has 63 possible skirt and top combinations so let's add the shoes.  First pair of shoes makes 63 possible skirt, top and shoe combinations. Next pair means 63 more.  This will happen 10 times because there are 10 pairs of shoes.  So 10 seta of 63 or 10 x 63=630

 

Continue this process with the necklaces and bracelets and you should get your answer.

 

Answer 2

When multiple variables may have multiple, independent values, you may multiply the number of possible values (just like 000 to 999 has 10*10*10 possibilities).

 

Now, we must determine that Jenny must wear one and only one each: a skirt, a top, a pair of shoes, a necklace and a bracelet.  That is, 0 of any item or multiple of any item is not allowed.  That makes the possibilities:

    9*7*10*2*5 = 6300 unique outfits         (note: if 0 of anything is allowed, add 1 to that value)