The answer to this question is 5775 different ways.
- Number of ways 4 can be selected from group of 12 is C(12,4)
- Number of ways 4 can be selected from group of remaining 8 is C(8,4)
- Number of ways 4 can be selected from group of remaining 4 is C(4,4)
So total number of ways can be calculated
C(12,4)*C(8,4)*C(4,4)
= 495*70*1
= 34650
So 3 groups are formed and the order of the selected group is not important. Therefore:
Total number of ways = 34650 / 3! = 34650 / 6 = 5775
You can take a look the following questions and try to solve it as well.
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In how many ways can 20 students be grouped into 3 groups?
The answer is 1140.
The number of ways that students can be grouped into 3 group is C(20,3) = 1140
How many groups of 2 can be made from 8?
The answer is 28.
Groups of 2 can be made from 8 is C(8,2) = 28
In how many ways can you divide 10 persons into three groups having 2, 3, and 5 persons?
A) 2520
B) 3628800
C) C(10,2)*C(10,3)*C(10,5)
D) P(10,2)*P(10,3)*P(10,5)
The answer to this question is C.
Given that 10 persons divide into three groups having 2,3, and 5 persons.
C(10,2)*C(10,3)*C(10*5) = 45*120*252 = 1360800
How many combinations ways can you choose 4 distinct groups of 3 students from total 12 students?
The answer is 369 000 combinations.
In how many ways can 10 students be grouped into 2 groups?
The answer is 45.
The number of ways 10 students can be grouped into 2 groups is C(10,2) = 45.