Question

Combinations question:

There are 6 employees working for a company in 6 different locations. After one year, all 6 employees must change their work location.

The new location for each employee is randomly chosen. Every location recieves exaclty one employee.

What are the possibilities for:

a) all employees recieve their old working location back.

b) no employee recieves his old working location.

c) exaclty one employee recieves his old working location.

Answer 1

We are given

n = 6

p = 1/6 = 0.166666667

q = 1 – p = 1 - 0.166666667 = 0.833333333

We have to use binomial distribution.

P(X=x) = nCx*p^x*q^(n – x)

What are the possibilities for:

a) all employees recieve their old working location back.

We have to find P(X=6)

P(X=6) = 6C6*0.166666667^6*0.833333333^(6 – 6)

P(X=6) = 6C6*0.166666667^6*0.833333333^0

P(X=6) = 1*0.166666667^6*1

P(X=6) = 0.000021433471

Required probability = 0.000021433471

b) no employee recieves his old working location.

We have to find P(X=0)

P(X=0) = 6C0*0.166666667^0*0.833333333^(6 – 0)

P(X=0) = 1*1*0.833333333^6

P(X=0) = 0.334897976

Required probability = 0.334897977

c) exaclty one employee recieves his old working location.

WE have to find P(X=1)

P(X=1) = 6C1*0.166666667^1*0.833333333^(6 – 1)

P(X=1) = 6C1*0.166666667^1*0.833333333^5

P(X=1) = 6*0.166666667*0.833333333^5

P(X=1) = 0.401877572

Required probability = 0.401877572