Understanding Combinations in Probability

The video tutorial explains the concept of combinations in probability, highlighting the difference between permutations and combinations. It provides examples, such as selecting students to pick up books and an IRS agent auditing tax returns, to illustrate how combinations work when order is not important. The tutorial also demonstrates the use of the combination formula and how to calculate it using a calculator.

What is the key difference between permutations and combinations?

• Neither consider order.

• Both consider order.

• Combinations consider order, permutations do not.

• Permutations consider order, combinations do not.

In a group of 10 students, how many are chosen to pick up books?

• 3 students

• 5 students

• 2 students

• 4 students

What is the formula used to calculate combinations?

• n! * r!

• n! / [(n-r)! * r!]

• n! / r!

• n! / (n-r)!

How many different ways can 3 students be chosen from a group of 10?

• 90 ways

• 150 ways

• 120 ways

• 60 ways

What is the factorial of 10?

• 3,628,800

• 3,628,000

• 3,600,000

• 3,000,000

What does the 'n' represent in the combination formula nCr?

• Number of choices

• Total number of items

• Number of combinations

• Number of permutations

In the IRS scenario, how many tax returns are flagged?

• 10 returns

• 12 returns

• 22 returns

• 20 returns

How many tax returns does the IRS agent need to audit?

• 12 returns

• 10 returns

• 20 returns

• 15 returns

What is the total number of ways the IRS agent can choose 12 returns from 22?

• 600,000 ways

• 646,646 ways

• 500,000 ways

• 700,000 ways

Why is a calculator used in the IRS scenario?

• To handle large numbers

• To simplify the process

• To verify the result

• To check for errors