Question

In how many ways can five people be divided into three groups

Answer 1

In how many ways can five people be divided into three groups?

Step-by-step explanation:

• Five people can be grouped into 3 groups in the following manners: 1,1,3 or 1,2,2.

• Therefore calculating the ways of dividing 5 people into 3 groups,

⇒(5! / 3!) ×  (1/2!) + (5! / (2!)²) + [ 3! / ( 2! 1! ) ] + (1/2!)

The values of ,

5! =  5 × 4 × 3 × 2 ×1 = 120

3! = 3 × 2 × 1 = 6

2! =2 × 1  = 2

1! = 1

Substituting the values,

⇒ (5! / 3!) ×  (1/2!) + (5! / (2!)²) + [ 3! / ( 2! 1! ) ] + (1/2!)

⇒ [ 120 / 6 × 2 ]+ [ 120/ 2 ×6 ] +[ 6/2] × [1 / 2 ]

⇒ 10 +30/2

⇒ 10 + 15

= 25

Therefore, there are 25 ways we can divide five people into three groups.