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Chapter 1: Q.1.28 (page 16)

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

Short Answer

Expert verified

(a)65530-- the basic principle of counting

(b)2520- use the multinomials.

Step by step solution

01

Given Information.

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

02

Part (a) Explanation.

Divide 8people among 4schools

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

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

localid="1649848745500" 4路4路4路4路4路4路4路4=48=65536different divisions of the teachers.

03

Part (b) Explanation.

Every school gets preciseness 2teachers:

To divide 8different objects into four groups of fixed sizes2,2,2and2.

localid="1649848759459" 82,2,2,2=8!2!2!2!2!=2520.different divisions of the teachers.

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