How many ways can you split 12 people into 3 teams of 4?

Solution:

We will be using the concept of permutations and combinations to solve this.

2 people into 3 teams of 4.

We know, ⁿC_r = n! / [(n - r)! × r!]

No. of ways to select the first 4 people for the first group = ¹²C₄ = 12! / [(12 - 4)! × 4!] = 12! / [(8! × 4!)] = 495

No. of ways to select 4 people from the remaining 8 for the second group = ⁸C₄   = 8! / [(8 - 4)! × 4!] = 8! / [(4! × 4!)] = 70

No. of ways to select 4 people from 4 for third group = ⁴C₄  = 4! / [(4 - 4)!] × 4!] = 4! / [(0! ×4!)] = 1

Total no. of ways to select people for group = (495 × 70 × 1) / 3! = 34650 /6 = 5775

Thus, you can split 12 people into 3 teams of 4 in 5775 different ways.

How many ways can you split 12 people into 3 teams of 4?

Summary:

You can split 12 people into 3 teams of 4 in 5775 different ways.