Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hello I'm currently self-teaching myself A-level maths but I seem to be stuck a little on pascal sequences and nCr.Could someone please give me a brief explanation??.Also what is nCr=0C1 ?If I apply the factorial formula it is
    0!/1!(0-1)!=0!/1!(-1)! but there is no negative factorial.So is it undefined??
    I would really appreciate your help!
    Offline

    3
    ReputationRep:
    (Original post by irenee)
    Hello I'm currently self-teaching myself A-level maths but I seem to be stuck a little on pascal sequences and nCr.Could someone please give me a brief explanation??.Also what is nCr=0C1 ?If I apply the factorial formula it is
    0!/1!(0-1)!=0!/1!(-1)! but there is no negative factorial.So is it undefined??
    I would really appreciate your help!
    Firstly, I find it cool that you're self-teaching A-Level maths. I dunno, I always find it cool when I hear people self-teach stuff.

    Anyways, this is binomial expansion and it relates to the pascal triangle. Do you know how to construct it? You start with 1 and then on each row, add the two numbers that are diagonally above it; treat blanks as zero.

    nCr is a function that tells us how many ways are there of choosing r elements (ignoring the order) from a set of a n.

    For instance for (a + b)3 how many ways can I obtain a b2 term?
    Well, (a + b)3 = (a + b)(a + b)(a + b)

    Now notice that there are 3 ways to get that b2 term.
    (a + b)(a + b)(a + b) = b2...
    (a + b)(a + b)(a + b) = b2...
    (a + b)(a + b)(a + b) = b2...

    This relates to Pascal's Triangle. Treat the first row as 0. Look at the third row (because 3 is our exponent of the entire bracket). Now look at the 2nd term, (because 2 is our exponent of the term we want). You'll find that this term is also 3.

    And if you do it via nCr, i.e. 3C2 = 3

    There is no point in doing 0C1 . Remember that n refers to our exponent of the bracket. If you're saying n = 0, then you're raising something to the power of 0.
    What's anything to the power of 0? It's just 1, so the reason it doesn't work is because there's no other terms, it's only just 1.

    As for your last point, negative factorials are undefined yes. This is because
    -1! = -1 x -2 x -3 x -4 x -5 .... x - infinity.
    However, it is possible to use this nCr method for negative exponents (and therefore involving negative factorials) however, I think I'll leave that until later. I hope that this sufficed as answer for now.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Thank you so much for your kind words and your comprehensive explanation.It was exactly what I was looking for.All is clear now thank youuuuuu
 
 
 
Poll
Do you think parents should charge rent?
Help with your A-levels

All the essentials

The adventure begins mug

Student life: what to expect

What it's really like going to uni

Rosette

Essay expert

Learn to write like a pro with our ultimate essay guide.

Uni match

Uni match

Our tool will help you find the perfect course for you

Study planner

Create a study plan

Get your head around what you need to do and when with the study planner tool.

Study planner

Resources by subject

Everything from mind maps to class notes.

Hands typing

Degrees without fees

Discover more about degree-level apprenticeships.

A student doing homework

Study tips from A* students

Students who got top grades in their A-levels share their secrets

Study help links and info

Can you help? Study help unanswered threadsRules and posting guidelines

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.