Chapter 9 Binomial Expansion

Question 1

What is the formula for n factorial (n!) ?

Answer 1

n! = n × (n - 1) × (n - 2) × … × 3 × 2 × 1

0! = 1

Question 2

What are binomial coefficients denoted by?

Answer 2

Binomial coefficients are denoted by nCr or can be found using Pascal’s triangle, using your calculator or using the formula

Question 3

What is the binomial expansion of (1 + x)^n?

Answer 3

The binomial expansion can be written as

Question 4

What is the general form of the binomial expansion?

Answer 4

This can be generalised as

Question 5

What is the number of ways to arrange n unlike objects in a line?

Answer 5

The number of ways to arrange n unlike objects in a line is n!

Question 6

What is the number of permutations of r objects from n?

Answer 6

The number of permutations of r objects from n is given by nPr = n! / (n - r)!

Question 7

What is the number of combinations of r objects from n?

Answer 7

The number of combinations of r objects from n is given by C(n, r) = n! / (r!(n - r)!)

Question 8

What is the difference between permutations and combinations?

Answer 8

For permutations, the order matters. For combinations, it does not.