Probability questions? (Middle school lvl)?

Question

Forgot how to do questions like these:

"A baseball team has 5 players that can play both 1st and 2nd base. How many different arrangements of these players could the coach use to play 1st and 2nd base?"

"A snack machine has 2 kinds of fruit, 3 kinds of chips, and 6 kinds of drinks. If len buys 1 piece of fruit, 1 bag of chips, and 1 drink, how many combinations can he choose from?"

"Suppose you flip a fair coin four times. What is the probability that you will get four tails? Write the probability as a fraction."


*How to do them, and answers? Thank you.

Answer 1

For probability questions in which you 'use up' one of your choices (i.e. the person can't be on both bases so they are used up if they are chosen for first and cannot also be on 2nd) you solve it by multiplying x factorial or x!. In the case of problem one it would be 5*4 or 20

For questions where you don't 'use it up but you have distinct choices working together you would multiply the choices together. In the case of problem 2 it would be 2*3*6 or 36

For the coin you have a 1 of 2 or 1/2 chance of getting a tail. Each flip is independent of the others so you multiply. 1/2 *1/2*1/2*1/2 or 1/16

Answer 2

I think the last one is 4/8

Answer 3

2) C(2;1)*C(3;1)*C(6;1)=2*3*6=36

3) 1/2*1/2*1/2*1/2=1/16