Probability and Counting Principles

This video tutorial explores probability problems involving permutations and combinations. It begins with a review of the probability formula and then delves into various examples. The first example calculates the probability of two people sitting next to each other at a round table. The second example determines the probability of forming an odd three-digit number from a set of digits. The third example examines the probability of selecting three consonants from the word 'teamwork'. The final example involves selecting a sample of people with specific gender criteria. Each example is explained step-by-step, highlighting the use of permutations and combinations in probability calculations.

What is the formula for calculating the probability of an event?

• Number of favorable outcomes multiplied by total number of outcomes

• Number of total outcomes divided by favorable outcomes

• Number of favorable outcomes divided by total number of outcomes

• Number of total outcomes minus favorable outcomes

In a round table seating arrangement, how do you calculate the total number of arrangements for six people?

• 6 factorial

• 5 factorial

• 4 factorial

• 3 factorial

When considering Mel and Dave as a single unit, how many groups are formed for the seating arrangement?

• 6 groups

• 5 groups

• 4 groups

• 3 groups

What is the probability that Mel and Dave are seated next to each other?

• 2/5

• 1/5

• 3/5

• 4/5

How many digits are available to form a three-digit number in Example 2?

• 7 digits

• 8 digits

• 6 digits

• 5 digits

Which digits can be used as the last digit to form an odd number?

• 3, 5, 7, 9

• 0, 2, 4, 6

• 2, 4, 6, 8

• 1, 3, 5, 9

What is the probability of forming an odd three-digit number?

• 6/7

• 5/7

• 4/7

• 3/7

How many letters are in the word 'teamwork'?

• 8 letters

• 7 letters

• 6 letters

• 9 letters

How many consonants are in the word 'teamwork'?

• 4 consonants

• 6 consonants

• 5 consonants

• 3 consonants

What is the probability of selecting three consonants from 'teamwork'?

• 4/7

• 5/7

• 3/7

• 2/7