Question

3 fill in the blank 2 points when creating a bitmoji, there are 10 options for eyes, 6 options for noses, 5 for mouths, and 3 for ears. how many possible bitmoji faces are there? choose your answer. based on your previous answer, if you have a bitmoji, and if your little brother makes a bitmoji selecting each body part randomly, whats the probability that his bitmoji will have the same face as yours? (enter your answer as a fraction.) type your answer. 4 fill in the blank 2 points in a 3 - player board game, each player starts by rolling a standard six - sided die. how many different combinations of starting rolls could there be? hint: think about each player individually and how many different rolls they could get, then how many ways those rolls could be put together. type your answer. using your answer from above, what is the probability that all three players roll the same number to start the game? (you do not need to reduce the fraction, although you may.) type your answer. hint: think about how many different combinations of rolls there could be, and how many combinations there are where all players rolled the same number. enter your answer as a fraction.

Explanation:

3.

Step1: Calculate number of bit - moji faces

Use the counting principle. Multiply the number of options for each feature. The number of ways to create a bit - moji face is the product of the number of options for eyes, noses, mouths, and ears.
$10\times6\times5\times3$
$=10\times90$
$ = 900$

Step2: Calculate probability of identical bit - moji

The probability that the little brother makes the same bit - moji is $\frac{1}{900}$ since there is 1 favorable outcome (matching your bit - moji) out of 900 total possible bit - moji faces.

Step1: Calculate number of combinations of die rolls

Each player has 6 possible rolls. By the counting principle, the total number of combinations of starting rolls for 3 players is $6\times6\times6=216$

Step2: Calculate probability of all players rolling the same number

There are 6 cases where all players roll the same number (all 1s, all 2s, all 3s, all 4s, all 5s, all 6s). The probability is $\frac{6}{216}$

Answer:

900
$\frac{1}{900}$

4.