Binomial question. (1 Viewer)

[Brad]

Hey any help would be nice, i know ive done this question before but its shitting me now as i can't get it, the answer should be:
n=14

its Find n if the coefficients of x^5 and x^6 in the expansion of:

(3+2x)^n have the same value.


I know its prob simple but its giving me the shits

 

[Affinity]

the coefficient of x^5

is 3^(n-5)*2^5 * (n C 5)

that for x^6 is

3^(n-6)*2^6*(n C 6)

since they are equal, divide the first by second, and you should get 1

so

[3(n C 5)]/[2(n C 6)] = 1

3n!/5!(n-5)! = 2n!/6!(n-6)!

simplifying

2(n-5) = 18

n-5 = 9, n=14

 

[Brad]

Thanks, that sorta what i got, but how did you simplify that bit at the end?

 

[Affinity]

(n-5)! = (n-6)!*(n-5)

 

[Brad]

Yeah, i was just looking at it and i figured it out, thanks a heap Affinity. Assesment task tomorrow