How I solve for distinct pairs or combinations? please help!

[Madoame]

My teacher told me to find how many combinations here. Is there another way other than writing all the possibilities?

Let A=(0,1,2,3,4,5) and B=(6,7,8,9)
How many distinct pairs are in A x B?

 

[DrPhil]

My teacher told me to find how many combinations here. Is there another way other than writing all the possibilities?

Let A=(0,1,2,3,4,5) and B=(6,7,8,9)
How many distinct pairs are in A x B?

There are six possible choices for A. Whatever is chosen for A, there are four different choices for B (no duplicated numbers). If you just imagine writing down all the combinations, you could write them in an array with six rows and four columns. The total number of possibilities is:
6 × 4 = . . .

 

[HallsofIvy]

This is an example of the "fundamental theorem of counting". If one event can happen in "m" ways and another can, for each of those, happen in "m" ways, they can both happen in mn ways. Here you can choose the first member from A in 6 ways, then, whatever the first member is, choose the second member from B in 4 ways and so can choose the two numbers in 6(4)= 24 ways, as Dr. Phil said.