SOLUTION: In how many ways can a group of 12 policemen group into 3 groups of 7, 3 and 2

Algebra ->  Permutations -> SOLUTION: In how many ways can a group of 12 policemen group into 3 groups of 7, 3 and 2       Log On


   

Question 815307: In how many ways can a group of 12 policemen group into 3 groups of 7, 3 and 2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There are 66 ways to chose 2 out of a group of 12 if the order in which they are chosen does not matter:12%2A11%2F2=66 .

There are 120 ways to chose 3 from the remaining 10,
12-2=10 ,
if the order in which they are chosen does not matter:
10%2A9%2A8%2F3%2F2=120 .

For each of the calculations above the math jargon is combinations of m elements taken from a set of n elements, calculated as n%21%2F%28n-m%29%21m%21=

So, there are 7920 ways to take a group of 2 and a group of 3 out of 12, leaving a group of 7 remaining:
66%2A120=highlight%287920%29 .