- #1
Matejxx1
- 72
- 1
Homework Statement
There are 30 students in a class. In how many ways can we arrange them if :
a)we must have three group, group one must have 5 students , group two 10 students and group three 15 students. [tex]answer=\frac{30!}{5!*10!*15!}[/tex]
b)we must have three group and all must have 10 students
[tex]answer= \frac{30!}{10!*10!*10!*3!}[/tex]
Homework Equations
[tex]C^r_n = \frac{n!}{r!*(n-r)!}[/tex]
[tex]V^r_n = \frac{n!}{(n-r)!}[/tex]
[tex]P_n= {n!}[/tex]
The Attempt at a Solution
a)
Okay so I'm not sure if the way I solved a) is correct, as I didn't get the exact same result as I should have .
what I tried doing was: to first pick 5 students out of those 30 so I got
[tex]C^5_{30} = \frac{30!}{5!*(25)!}[/tex]
and then I did the same for the other 2 groups
[tex]C^{10}_{25} = \frac{25!}{10!*(15)!}[/tex]
[tex]C^{15}_{15} = \frac{15!}{15!*(0)!}[/tex]
and then I multiplied all the 3 combinations together and got
4.66*1011
which is the right answer but not the same one as in the textbook.
b) I tried doing the same thing as with a)
[tex]C^{10}_{30} = \frac{30!}{10!*(20)!}[/tex]
[tex]C^{10}_{20} = \frac{20!}{10!*(10)!}[/tex]
[tex]C^{10}_{10} = \frac{10!}{10!*(0)!}[/tex]
and the result comes out completely wrong
I am wondering now if somebody could help me figure a) out and kinda of point me in the right direction with b)
thanks