Math Help - [SOLVED] binomial distribution problem

1. [SOLVED] binomial distribution problem

n=7,r=3,p=0.25
Pr= 7!/3!(7-3)!=1(0.25)^3(1-0.25)^4 =0.004943848.
Why is this answer wrong ?
The correct answer is 0.173035

2. Originally Posted by chaosx
n=7,r=3,p=0.25
Pr= 7!/3!(7-3)!=1(0.25)^3(1-0.25)^4 =0.004943848.
Why is this answer wrong ?
The correct answer is 0.173035
For the Binomial distribution:

$Pr(X=r)={n \choose r}p^r(1-p)^{n-r}$

so in this case:

$Pr(X=3)={7 \choose 3}\,0.25^3\,0.75^4=\frac{7!}{3!\,4!}\,0.25^3\,0.75 ^4=0.173035$

RonL