Question

Find the coefficient of \( a^3b^{10} \) in the expansion of \( (a+b)^{13} \)

Answer 1

@SmoothMath can u help me

Answer 2

Hint: Pascal's Muthaflutterin' triangle. Google that ish.

Answer 3

lol

Answer 4

Here n= 13

you want coefficient of : \(a^3b^{10}\)

So find:

\[\large ^{13}C_{10}\]

This will be the coefficient..

Answer 5

I am getting 286 which isnt a number on pascals triangle

Answer 6

\[\large ^{13}C_{10} = \frac{13!}{(13-10)! \times 10!} = \frac{13 \times 12 \times 11}{3 !} \implies 13 \times 2 \times 11\]

Answer 7

but check on pascals triangle there is no 286 by 13

Answer 8

http://britton.disted.camosun.bc.ca/pascal/pascal.html

Answer 9

Okay I will check..

Answer 10

See:

According to me it is:

\[\\large \^\{\1\3\}C_\{\1\0\}\\]

Answer 11

ya that is what i thought tooo

Answer 12

U know what ill sleep over it and continue it tom. Its nearly 4 am and i gotta be up early. A new day bring new surprises

Answer 13

do you have answer with you for this question??

Answer 14

nope i dont

Answer 15

Ill just sit over it tom

Answer 16

Wait I tell you all the values of triangle for n = 13..

Answer 17

yaaaaa like i am assuming that it is 186

Answer 18

No..

Answer 19

thats the one that makes most sense

Answer 20

no I got the answer..

13th row contains 286..

Answer 21

hmmmm

Answer 22

http://wiki.answers.com/Q/What_is_row_13_in_pascal's_triangle

Answer 23

oh ya it does i guess its a mistake on that website

Answer 24

alrighty thanks guys Gnite

Answer 25

Yes there is a mistake..

Good Night @swissgirl

Answer 26

ohhhhhhh ok Thankss

Answer 27

Welcome dear..

Answer 28

Sorry there will come 286 in place of 186 in the link you provided..

last one is 13th row there..

Answer 29

An easier method that I would use than the pascals triangle is the Binomial Expansion: \((a+b)^{n} = \binom{n}{r}
*(a)^{n-r}b^{r}\)
\[\binom{13}{r} *(a)^{13-r}*b^{r} \]
\[\text{So you are looking for} ~a^{3}b^{10} then ~r = 10 \]
\[\binom{13}{10} *(a)^{13-10}*b^{10} => 286a^3b^{10}\]
Well this is an easier method to me than using the Pascals traingle which is confusing

Answer 30

And the answer is correct; you can check it here:
http://www.wolframalpha.com/input/?i=%28a%2Bb%29^13