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Statistics 1 Week 6

Mathematical Concepts

📚

Important concepts

Simultaneous and Non-Simultaneous Events

Simultaneous events occur at the same time, such as rolling two dice together. Non-simultaneous events occur one after the other, like rolling one die, noting the result, and then rolling another die.

Events with and without Repetition

Events with repetition allow the same event to happen more than once, like drawing a card from a deck, replacing it, and drawing again. Events without repetition do not allow the same event to happen more than once, like drawing a card from a deck and not replacing it before drawing again.

Combination and Permutation

Combinations are used when the order does not matter, such as choosing 3 fruits from a basket of 5 different fruits. Permutations are used when the order matters, such as arranging 3 books out of 5 on a shelf.

Examples

Combinations

  • Choosing 3 students from a class of 10.
  • Selecting 2 flavors of ice cream from 5 available flavors.
  • Picking 4 cards from a deck of 52 cards.
  • Choosing 5 books from a shelf of 8 books.

Permutations

  • Arranging 3 books out of 5 on a shelf.
  • Assigning 4 different tasks to 4 employees.
  • Arranging 5 different flowers in a row.
  • Creating a 3-digit code using numbers 1 to 9.

Card Suits

Spade: ♠

Heart: ♥

Diamond: ♦

Club: ♣

Card Selection Problems

I few examples here practice more question similar to it, its more than enough

Q.Number of ways to choose 4 Kings and 4 Queens: 1

Formula: C(4, 4) × C(4, 4) = 1 × 1 = 1

Explanation: There is only one way to choose all 4 Kings and all 4 Queens since you are choosing all available cards of each type.

Q.Number of ways to choose 1 King and 1 Queen: 16

Formula: C(4, 1) × C(4, 1) = 4 × 4 = 16

Explanation: You can choose any 1 King from 4 Kings and any 1 Queen from 4 Queens. So, there are 16 different ways to choose 1 King and 1 Queen.

Q.Number of ways to choose 1 King or 1 Queen: 8

Formula: C(4, 1) + C(4, 1) = 4 + 4 = 8

Explanation: You can choose any 1 King from 4 Kings or any 1 Queen from 4 Queens. So, there are 8 different ways to choose either 1 King or 1 Queen.

Q.Number of ways to choose Ace cards: 4

Formula: C(4, 1) = 4

Explanation: You can choose any 1 Ace from 4 Aces. So, there are 4 different ways to choose an Ace card.

Selection of a Team

When selecting a team, combinations are typically used because the order in which team members are chosen does not matter. For example, if you need to select a team of 3 members from a group of 10, you would use the combination formula:

C(10, 3) = 120

This means there are 120 different ways to choose 3 members from a group of 10.

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