Help

1.Rachel draws three cards from a standard deck of cards, one at a time. How many different ways can she draw three cards? (The order of the cards matters.)

52 ways to select first card x 51 ways to select the 2nd card x 50 ways to select the last card  = 132,600 ways

2.Rachel draws three cards from a standard deck of cards, one at a time. However, this time, she puts each card she drew back into the deck. How many different ways can she draw three cards? (The order of the cards matters.)

There are  52 ways to select each card so.....52^3  = 140,608 ways

3.Joe wants to find all the four-letter words that begin and end with the same letter. How many combinations of letters must he examine? A word is any sequence of letters, such as MTHM, and does not have to be English.

If the middle two letters can be anything...then

He has 26^3  = 17576 possible "words"

26 ways to choose each of the first three letters ....the last letter is pre-determined by the first letter

4.There are 19 figure skaters in the Olympic women's competition, including 3 Americans. The gold medal goes to first place, silver to second, and bronze to third.
In how many ways can the medals be awarded to three of the 19 figure skaters?

We have a possibility of 19 first place competitors....then 18 possible second place competitors ...and 17 possible third place competitors....so

19 x 18 x 17  = 5814 ways