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

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

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

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

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?

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

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

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

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

From 12 students, three are chosen as captain, vice-captain, and team member (distinct roles). Find the number of ways both by direct permutation and by combination then multiplication by factorial.

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