Question Type 7: Writing scenarios as both permutation and combination Exercises

In how many ways can a committee of 5 people be chosen from a group of 20, where roles on the committee are identical?

In how many ways can 6 students be seated in a row of 6 chairs?

A secure lock code consists of 4 distinct digits chosen from 0–9. How many possible codes are there?

How many ways can you choose 4 pizza toppings from 10 available toppings, if order does not matter?

From 15 job applicants, 5 will be shortlisted and then ranked from 1 to 5. Find the total number of possible ranked shortlists.

A club has 10 members. How many ways can it choose a president and a vice-president?

How many ways can 5 cards be drawn from a 52-card deck and then arranged in an ordered sequence?

How many ways can you award gold, silver, and bronze medals to three distinct winners chosen from 20 participants?

In how many different ways can 8 distinct books be arranged in a row on a shelf?

A teacher chooses 2 teaching assistants out of 6 and assigns one to grade exams and the other to record marks. How many assignments are possible?