How many combinations are possible with $1$ item from $6$ different groups?

Question

I am trying to figure out how to get the total number of combinations of $1$ item from $6$ different groups with a different number of variables for each group.

• Group $1$: $60$ variables (Apples, Oranges, Pears...)
• Group $2$: $2$ variables (Yes, No)
• Group $3$: $13$ variables $(1, 2, 3...)$
• Group $4$: $12$ variables (Monday, Tuesday, Wednesday...)
• Group $5$: $6$ variables (Red, Green, Blue...)
• Group $6$: $15$ variables (Run, Swim, Dive...)

Each result would have $1$ item from each group i.e. (Apples, Yes, $2$, Wednesday, Blue, Swim). How many different combinations are possible?

Answer 1

The answer is simply: $$60\times2\times13\times12\times6\times15$$

Let us start with just $2$ groups: the first two groups.

For each element in the $1^{st}$ group, there are (number of elements in $2^{th}$ group) ways to choose.

Therefore, it is (number of elements in $1^{th}$ group) * (number of elements in the $2^{th}$ group).

Repeat this for an indefinite amount of groups.