Answer:
(a) 65536 - the basic principle of counting
(b) 2520 - use the multinomials.
Step-by-step explanation:
Divide 8 people among 4 schools
The teachers are different among themselves, and so are the schools.
(a)
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
Note: this does not ensure that every school gets a teacher
(b) - <u>Every school gets precisely 2 teachers:</u>
to divide 8 different objects into four groups of fixed sizes 2, 2, 2 and 2, use the multinomial coefficient
( 8 2, 2, 2, 2) = (8!)/(2!2!2!2!) ==> 2520
different divisions of the teachers
