# 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?

Jul 29, 2016

$77$

#### Explanation:

Each of the $7$ can have $11$ different toppings so let us denote each of the yogurts as ${y}_{i} | 1 \le {y}_{i} \le 7$ and each of the toppings as ${y}_{j} | 1 \le {t}_{i} \le 11$

then we know for the first two yogurts ...
${y}_{1} \rightarrow {t}_{1}$
${y}_{1} \rightarrow {t}_{2}$
$\ldots$
${y}_{1} \rightarrow {t}_{11}$
Next
${y}_{2} \rightarrow {t}_{1}$
${y}_{2} \rightarrow {t}_{2}$
$\ldots$
${y}_{2} \rightarrow {t}_{11}$

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

$7 \cdot 11 = 77$ possible choices

May 17, 2018

$7 \times 11 = 77$

#### 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:

$7 \times 11 = 77$