expansions

Question 1

nCr Gen

Answer 1

number (power) choose row. This will give you a number on pascals triangle. For example 5C3 will give you the number that is 5 levels down and 3 across. (if r is ever 0 then it will give you 1, if it is ever 1 then it will be equal to n)

Question 2

nCr equation

Answer 2

n!/r!(n-r)!

Question 3

What is a factorial? (!)

Answer 3

A number timesed by all lower integers going down to 1.
Eg. 4!= 432*1

Question 4

how do you find nCr on calculator?

Answer 4

Matrix (1)
OPTN
F6
PROB

Question 5

(x+y)^2

As an example of how to expand brackets.

Answer 5

(2C0) y^0 x^2 + (2C1) y^1 x^1 + (2C2) y^2 x^0

One factor is multiplied from an order going from 0 to n and the other does the same but going from n to 0.

Question 6

What would a term be in an expanded (1-x)^2

Answer 6

nCr*χ^(n-r)

Question 7

How do you calculate percentage error (bear with me sorry)

Answer 7

(100 (actual - estimate))/actual

Question 8

using (1-x)^n how could you go about estimating 0.97^5?

Answer 8

0.97= (1-0.03)
0.97^5=(1-0.03)^5
x= -0.03
0.97^5= 5C0χ^5 + 5C1χ^4 +… 5C5χ^0

this except because its an estimate you dont have to calculate all of the terms. That’s what the percentage error is about.

Question 9

What is a permutation?

Answer 9

What you need to know is that it’s relevant when the order matters.

Question 10

Number of ways to arrange n different objects is?

Answer 10

n!

Question 11

nPr Gen

Answer 11

Choose r from n when order matters (permutation).
This keeps part of a factorial eg.
4!= 4* 3 * 2 * 1
4P2= 4 * 3

Question 12

nPr equation

Answer 12

n!/(n-r)!

Question 13

how to turn nPr into nCr just in case?

Answer 13

divide by r!