Question

A yogurt shop sells `7` flavors of frozen yogurt and `11` different toppings. How many choices are possible for a single serving of frozen yogurt with one topping?

Answer 1

`77`

Explanation:

Each of the `7` can have `11` different toppings so let us denote each of the yogurts as `y_i | 1<=y_i<=7` and each of the toppings as `y_j | 1<=t_i<=11`

then we know for the first two yogurts ...
`y_1 rightarrow t_1`
`y_1 rightarrow t_2`
`...`
`y_1 rightarrow t_11`
Next
`y_2 rightarrow t_1`
`y_2 rightarrow t_2`
`...`
`y_2 rightarrow t_11`

so each one can be multiplied by the 11 different toppings so we have

`7*11 = 77` possible choices

Answer 2

`7xx11=77`

Explanation:

For the first flavour of frozen yogurt, there are `11` possible toppings, so this is already `11` different choices.

The same for the second flavour, there are `11` choices.

The same applies for each of the flavours....

Foe each different flavour there are `11` toppings, so the total number of different choices is:

`7 xx 11 = 77`