A store sells clothes for men. It has 3 kinds of jackets, 7 kinds of shirts, and 5 kinds of pants. Find the number ofways a person can buy: (a) one of the items; (b) one of each of the three kinds of clothes.

number(one of the items):

since there are 15 items , wouldn't that just be 15 ??

number of 3 kinds of clothing =3*7*5 = 105
or
C(3,1)*C(7,1)*C(5,1) = 3*7*5 = 105

(a) One of the items:

To find the number of ways to buy one item, we simply add up the number of choices for each type of clothing.

Number of choices for jackets = 3
Number of choices for shirts = 7
Number of choices for pants = 5

So, the total number of ways to buy one item is 3 + 7 + 5 = 15.

(b) One of each of the three kinds of clothes:
To find the number of ways to buy one of each type of clothing, we need to multiply the number of choices for each category.

Number of choices for jackets = 3
Number of choices for shirts = 7
Number of choices for pants = 5

So, the total number of ways to buy one of each of the three kinds of clothes is 3 x 7 x 5 = 105.

Therefore,
(a) There are 15 ways to buy one item.
(b) There are 105 ways to buy one of each of the three kinds of clothes... or you could say, "There are 105 ways to look like a fashion disaster!"

To find the number of ways a person can buy one of the items, you simply need to add up the number of options for each type of clothing.

a) Number of ways to buy one item:
3 kinds of jackets + 7 kinds of shirts + 5 kinds of pants = 15 ways

For the second part, to find the number of ways a person can buy one of each of the three kinds of clothes, you need to multiply the number of options for each type of clothing.

b) Number of ways to buy one of each of the three kinds of clothes:
3 kinds of jackets * 7 kinds of shirts * 5 kinds of pants = 105 ways

To find the number of ways a person can buy different combinations of clothes from the given options, we can use the concept of counting principles.

(a) Number of ways to buy one item:
In this case, we need to calculate the total number of options available (jackets, shirts, and pants) and add them together.
Total options = Number of jacket options + Number of shirt options + Number of pant options
= 3 + 7 + 5
= 15
So, there are 15 ways to buy one item.

(b) Number of ways to buy one of each of the three kinds of clothes:
To calculate the number of ways to buy one of each item, we need to multiply the available options of each kind of clothes together.
Number of ways = Number of jacket options × Number of shirt options × Number of pant options
= 3 × 7 × 5
= 105
So, there are 105 ways to buy one of each of the three kinds of clothes.