nCr and nPr(5m)

I need steps. thank you. 5 marks

1. There are 32 teams entering a soccer competition. They are divided into 8 groups (A-H) with 4 teams in each group for group stage. The top two teams in each group will enter he round of 16, and a list can be formed. How many different lists can be formed?

Solutions: 429 981 696


2. It is known that the password for an ATM card must be formed by 6 numbers from 0 to 9, and the numbers used can be repeated. Mr. Wong is going to choose 6 different numbers to form the password. A hacker tries to find out the password of Mr. Wong by trails and errors. It is given that the time required for testing one trail is 10^(-2) seconds. How long does the hacker take to find out the password of Mr. Wong in the worst case?

Solutions: 10,000 seconds.

3. Didi's mother has 6 different cartons of juice and 4 different cans of soft drinks. She puts 4 cartons of juice and 2 cans of soft drinks into the refrigerator in a row. Find number of arrangements.
Solutions: 64 800


4. In a lucky draw, 22 participants are male and 18 are female.
How many arrangements are there for 3 participants wining the first prize, second prize and third prize, given that exactly 2 winners out of 3 are male?

Solution: 24 948