rishianand7 wrote:In how many different ways can a group of 9 people be divided into 3 groups, with each group containing 3 people?
280
1260
1680
2520
3360
An alternate approach:
The FIRST PERSON selected must be combined with a PAIR of people to form a group of 3.
From the 8 OTHER PEOPLE, the number of pairs that be formed = 8C2 = (8*7)/(2*1) = 28.
6 people left.
The NEXT PERSON selected must also be combined with a PAIR of people to form a group of 3.
From the 5 OTHER PEOPLE, the number of pairs that can be formed = 5C2 = 10.
3 people left.
The NEXT PERSON selected must also be combined with a PAIR of people to form a group of 3.
From the 2 OTHER PEOPLE, the number of pairs that can be formed = 2C2 = 1.
To combine these options, we multiply:
28*10*1 = 280.
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