Combinatorics. Intro

I. Imagine you visit an apparel store. After some time you put your eye on 3 different shirts and 5 different trousers.

You like all of them, but you have money to buy only one piece of clothing. How many options do you have?

II. A friend of yours comes by. You have similar tastes, so she likes the same 3 shirts and 5 trousers as you do. She too has money to buy only one thing.

How many ways do you have to buy a piece of clothing for each one of you? (You may choose independently of each other)

III. After some fitting you realise that you don't want to wear the same things.

How many ways do you have to buy a piece of clothing for each one of you? (You are not allowed to buy the same shirt or the same trousers)

IV. A manager comes to you and says they have a special offer today. You may buy a shirt and get trousers for free.

How many options are there to pick a pair "shirt-trousers"?

V. You and your friend decide to use the offer, but you still don't want to wear the same shirt or trousers. So you have to choose different shirts and different trousers.

How many options do you have?