Q3W6 - FEB. 29, 2024 - FCT, Permutation & Combination

What is the counting principle in fundamental counting techniques?

• The counting principle states that if there are m ways to do one thing and n ways to do another, then there are m - n ways to do both things together.

• The counting principle states that if there are m ways to do one thing and n ways to do another, then there are m + n ways to do both things together.

• The counting principle states that if there are m ways to do one thing and n ways to do another, then there are m / n ways to do both things together.

• The counting principle states that if there are m ways to do one thing and n ways to do another, then there are m * n ways to do both things together.

Calculate 5 factorial.

• 120

• 30

• 100

• 25

How many permutations can be made from the letters A, B, C, D?

• 12

• 6

• 24

• 18

In how many ways can a committee of 3 be chosen from a group of 10 people?

• 15

• 6

• 50

• 120

Solve the following application problem: In how many ways can a president, vice president, and treasurer be chosen from a group of 10 people?

• 120

• 30

• 90

• 45

What is the probability of drawing 2 red balls and 1 blue ball from a bag containing 5 red balls and 3 blue balls?

• The probability is (5C2 * 3C1) / 8C3 = (10 * 3) / 56 = 30/56 = 5/28

• The probability is (5C2 * 3C1) / 8C3 = (10 * 3) / 56 = 30/56 = 15/28

• The probability is (5C2 * 3C1) / 8C3 = (10 * 3) / 56 = 30/56 = 1/28

• The probability is (5C2 * 3C1) / 8C3 = (10 * 3) / 56 = 30/56 = 15/28 + 1

A lock has 4 dials, each labeled with the digits 0-9. How many possible combinations are there if each digit can only be used once?

• 24

• 362880

• 5040

• 120

In how many ways can 4 books be arranged on a shelf?

• 10

• 24

• 12

• 6

If there are 6 people in a race, how many different ways can they finish in first, second, and third place?

• 6

• 120

• 720

• 24

A bag contains 8 green, 4 blue, and 3 red marbles. What is the probability of drawing 2 green and 1 blue marble?

• 0.008 or 0.8%

• 0.25 or 25%

• 0.75 or 75%

• 0.1123 or approximately 11.23%