Question Type 5: Solving simpler world problems involving combinatoric functions Bootcamps

If 12 people each shake hands exactly once with each other, how many handshakes occur?

How many ways can 5 students be selected from a class of 10 to form a committee?

A pizza place offers 6 toppings. A customer chooses 3 distinct toppings. How many different topping sets are possible?

How many ways can 3 people be seated in 5 distinct chairs?

A manager needs to assign 3 distinct tasks to 5 employees, giving exactly one task per employee. How many possible assignments are there?

In a lottery you choose 6 numbers from 1 to 49. How many distinct combinations are possible?

In a race of 8 runners, how many ways can first, second, and third place be awarded?

In how many ways can 4 different books be arranged on a shelf if only 3 positions are available?

How many binary strings of length 10 contain exactly 4 ones?

In a triangular race with 4 cars, only first and second places are awarded. How many possible podium finishes (first and second) are there?

How many distinct seating arrangements are there for 6 people around a circular table?

How many diagonals does a convex polygon with 20 vertices have?

How many binary strings of length 10 have at least 8 zeros?

From 8 men and 7 women, a team of 5 is to be formed with exactly 3 men and 2 women. How many such teams can be formed?

A security code consists of 4 distinct digits chosen from 0–9 with no repetition. How many codes are possible?

From 8 men and 6 women, a committee of 5 is formed with at least 2 women. How many ways?

In how many ways can you distribute 5 identical balls into 3 distinct boxes?

In a standard 52-card deck, how many 5-card hands contain exactly 2 aces?

A classroom has 4 round tables: two tables seat 3 students each and two tables seat 2 students each. If there are exactly 10 students and we only care about which table each student sits at (not the seat order), how many ways can they be assigned to tables?

There are 4 tables in a café: 2 tables seat 2 people each and 2 tables seat 1 person each. If 6 distinct customers arrive, in how many ways can the host assign them to tables (tables are distinct but seats at the same table are identical)?