Answer:
34650 ways
Explanation:
To choose for the first group
1st grouping
the number to select from is 12
and we want to group into 4
12C4= C(12,4)= 12!/4!(12-4)!
= 12!/4!8!
=12*11*10*9*8!/4!8!
=12*11*10*9/4*3*2*1
=11880/24
=495
2nd grouping
the number to select from is 8
and we want to group into 4
8C4= C(8,4)= 8!/4!(8-4)!
= 8!/4!4!
=8*7*6*5*4!/4!4!
=8*7*6*5*/4*3*2*1
= 1680/24
=70
3rd grouping
the number to select from is 4
and we want to group into 4
4C4= C(4,4)= 4!/4!(4-4)!
= 4!/4!
=1
495∗70∗1=34650 ways
the total number of ways to choose three groups, when group order matters is 34650 ways