Question Type 8: Applying permutations and combinations separately Bootcamps

In how many ways can 5 people be seated in a row of 5 chairs?

Calculate the number of ways to choose 3 books to read from 6 distinct books.

How many 4-digit codes can be formed using the digits 0–9 if no digit is repeated?

From 8 students, a president and a vice-president are to be selected. How many possible selections are there?

In a race with 20 runners, how many possible outcomes are there for first, second, and third places?

A committee of 5 is to be formed from 4 women and 6 men. How many ways are there to choose exactly 2 women and 3 men?

A lock uses a sequence of 3 letters (A–Z) followed by 2 digits (0–9). Letters may not repeat, but digits may repeat. How many distinct codes are possible?

A bag contains 8 red and 7 blue balls. If 5 balls are drawn at random, how many ways are there to draw exactly 3 red and 2 blue balls?

From 12 participants, a subcommittee of 4 is selected and then a chair and a secretary are chosen from that subcommittee. How many ways can this be done?

From 15 people, a team of 5 is selected and then the 5 team members are arranged in a line for a photograph. How many possible selections and arrangements are there?

A drawer has 5 green, 4 yellow, and 3 red marbles. If 4 marbles are drawn at random, how many ways result in at least one marble of each color?

From 100 students, 10 are chosen as finalists and then 3 of these finalists receive gold, silver, and bronze medals (distinct awards). How many distinct outcomes are possible?