Q.1.28 - A First Course in Probability

Question

If $8$new teachers are to be divided among $4$schools, how many divisions are possible? What if each school must receive $2$teachers?

Step-by-Step Solution

Answer

$\left(a\right) 65530$-- the basic principle of counting

$\left(b\right) 2520$- use the multinomials.

Step 1 Given Information.

Let $8$new teachers are to be divided among $4$schools.

Step 2 Part (a) Explanation.

Divide $8$people among $4$schools

The teachers are different among themselves, and so are the schools.

Every teacher can choose a school. By the basic principle of counting:

$4·4·4·4·4·4·4·4=4^8=65536$different divisions of the teachers.

Step 3 Part (b) Explanation.

Every school gets preciseness $2$teachers:

To divide $8$different objects into four groups of fixed sizes$2,2,2$ and2.

$\left(\begin{array}{c}8\\ 2,2,2,2\end{array}\right)=\frac{8!}{2!2!2!2!}=2520$.different divisions of the teachers.