Counting

Question 1

What are two counting techniques?

Answer 1

1.) Sum rule
2.) Product rule

Question 2

Mutual exclusive means

Answer 2

Events that can’t be done simultaneoulsy

Question 3

Sum Rule

Answer 3

If task T₁ and task T₂ can happen in n₁ and n₂ ways respectively and T₁, T₂ are mutually exclusive then any of the task can happen in n₁+n₂ ways.

Question 4

Product Rule

Answer 4

If task T₁ and task T₂ can happen in n₁ and n₂ ways respectively and T₁, T₂ are mutually exclusive then both or all the tasks can be happened in n₁n₂ ways

Question 5

remember for sum rule

Answer 5

either

Question 6

remember for product rule

Answer 6

all tasks or together

Question 7

Necessary condition for T₁, T₂ in sum rule or product rule

Answer 7

T₁ and T₂ are mutually exclusive

Question 8

A or B (in terms of counting techniques)

Answer 8

Generally A or B means AUB but if A and B are mutually exclusive then A∩B = Φ, then AUB becomes sum rule

Question 9

Word for permutation

Answer 9

Arrangement

Question 10

Permutation

Answer 10

Arrangement of r objects from n distinct objects linearly

Question 11

Types of permutation and also their formulas

Answer 11

1.) Without repetition
no. of ways = ⁿPᵣ = n! / (n-r)!
2.) With repetition
no. of ways = nʳ

Question 12

Special case for permutation

Answer 12

In without repetition,
When r = n
then no. of ways = n!

Question 13

value of 0!

Answer 13

1

Question 14

value of 1!

Answer 14

1