Still Confused?

Try reviewing these fundamentals first

- Home
- AU Year 12 Maths
- Permutations and Combinations

Still Confused?

Try reviewing these fundamentals first

Still Confused?

Try reviewing these fundamentals first

Nope, got it.

That's the last lesson

Start now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started Now- Lesson: 1a54:32
- Lesson: 1b10:52
- Lesson: 2a5:28
- Lesson: 2b1:03
- Lesson: 2c1:10
- Lesson: 2d10:06
- Lesson: 3a2:33
- Lesson: 3b6:26

A Pascal's triangle is a number triangle of the binomial coefficients. The first row of the triangle is always 1.

- 1.Expand:a)i) ${\left( {a + b} \right)^0}$ =

ii) ${\left( {a + b} \right)^1}$ =

iii) ${\left( {a + b} \right)^2}$ =

iv) ${\left( {a + b} \right)^3}$ =

Use Pascal's Triangle to expand:

i) ${\left( {a + b} \right)^4}$ =

ii) ${\left( {a + b} \right)^5}$ =b)Investigating Pascal's Triangle - 2.Pascal's Triangle - sum of numbers in each rowa)
Row Pattern Corresponding binomial expression Sum of the numbers in,the row Express the sum as a power of 2 1 1 ${\left( {a + b} \right)^0}$ 2 1 1 ${\left( {a + b} \right)^1}$ 3 1 2 1 ${\left( {a + b} \right)^2}$ 4 1 3 3 1 ${\left( {a + b} \right)^3}$ 5 1 4 6 4 1 ${\left( {a + b} \right)^4}$ : : : : : n ${\left( {a + b} \right)^{n - 1}}$ n+1 ${\left( {a + b} \right)^n}$ b)What is the sum of the numbers in the 10th row of Pascal's Triangle?c)What is the sum of the coefficients in the expansion of ${\left( {a + b} \right)^{50}}$ ?d)Express the number pattern of Pascal's triangle in "combination" form, then deduce the following formula:

$\;$ ${}_n^{}{C_0}$ + ${}_n^{}{C_1}$ + ${}_n^{}{C_2}$ + ${}_n^{}{C_3}$ + … + ${}_n^{}{C_{n - 2}}$ + ${}_n^{}{C_{n - 1}}$ + ${}_n^{}{C_n}$ = ${2^n}$ - 3.Without using a calculator, evaluate:a)${}_{10}^{}{C_0}$ + ${}_{10}^{}{C_1}$ + ${}_{10}^{}{C_2}$ + … + ${}_{10}^{}{C_9}$ + ${}_{10}^{}{C_{10}}$b)${}_5^{}{C_0}$ + ${}_5^{}{C_1}$ + ${}_5^{}{C_2}$ + ${}_5^{}{C_3}$ + ${}_5^{}{C_4}$

We have over 1040 practice questions in AU Year 12 Maths for you to master.

Get Started Now