Combinations and Their Applications

The video tutorial explains how to evaluate combinations using different notations, focusing on examples like 8 choose 6, 12 choose 9, and 12 choose 3. It covers the formula for combinations, N choose R, and its applications in binomial theorem, combinatorics, and probability. The tutorial provides detailed steps for calculating combinations, simplifying factorials, and understanding the equivalence of different combinations. The video concludes with a summary of the key points discussed.

What does the notation 'n choose r' represent in combinatorics?

• The number of ways to arrange n items from r items.

• The number of ways to select n items from r items with regard to order.

• The number of ways to select r items from n items without regard to order.

• The number of ways to arrange r items from n items.

Which of the following fields use combinations?

• Geometry

• Trigonometry

• Algebra

• Probability

What is the factorial representation of 8 choose 6?

• 8! / (6! x 2!)

• 8! / (4! x 4!)

• 8! / (7! x 1!)

• 8! / (5! x 3!)

How many different groups can be formed when choosing 6 people from 8?

• 14

• 28

• 56

• 70

What is the significance of the property 6 + 2 = 8 in the context of combinations?

• It ensures the combination is set up correctly.

• It is used to calculate permutations.

• It is a property of factorials.

• It is used to determine the order of selection.

What is the simplified result of 12 choose 9?

• 110

• 120

• 330

• 220

Which factorials are used in the denominator for calculating 12 choose 9?

• 11! and 1!

• 9! and 3!

• 8! and 4!

• 10! and 2!

What is the result of simplifying 2 x 11 x 10 in the context of 12 choose 9?

• 440

• 220

• 330

• 110

Why is 12 choose 3 equivalent to 12 choose 9?

• Because both involve the same number of calculations.

• Because 12 choose 3 is a permutation of 12 choose 9.

• Because choosing 3 from 12 is the same as leaving 9 out of 12.

• Because 12 choose 3 is a subset of 12 choose 9.

What is the result of 12 choose 3?

• 220

• 110

• 120

• 330