stats question

[sonney32]

40% of the customers that come into a discount store purchases something. Find the probability that 3 of the next 5 customers make a purchase. (binomial random variable)

(p) = 5!
---------------(.4)to the 3rd (.6) to 5-3
3!(5-2)!

5!
----------(.4)to the 3rd (.6) to the 2nd---
3!2!

5*4*3*2*1
------------(.4)to the 3rd (.6)tothe 2nd
(3*2*1)(2*1)

=10(.064)(.36)

=.2304

My question is how do they come up with (3*2*1)(2*1) of the problem, I do not know how they come up with this, and was hoping that I could get it explained to me so I can work on some of my problems.
Thanks.

 

[Deleted member 4993]

40% of the customers that come into a discount store purchases something. Find the probability that 3 of the next 5 customers make a purchase. (binomial random variable)

(p) = 5!
---------------(.4)to the 3rd (.6) to 5-3
3!(5-2)!

5!
----------(.4)to the 3rd (.6) to the 2nd---
3!2!

5*4*3*2*1
------------(.4)to the 3rd (.6)tothe 2nd
(3*2*1)(2*1)

=10(.064)(.36)

=.2304

My question is how do they come up with (3*2*1)(2*1) of the problem, I do not know how they come up with this, and was hoping that I could get it explained to me so I can work on some of my problems.
Thanks.

This is combination - number of ways you can choose 3 things from a set of 5 things. This sis expressed as:

\(\displaystyle _nC_r \ = \ \frac{n!}{r!*(n-r)!}\)