Nine-chairs-in-a-row-are-to-be-occupied-by-six-students-and-Prof-George-Prof-Pieter-and-Prof-John-These-three-professors-arrive-before-the-six-students-and-decide-to-choose-their-chairs-so-that-ea

Question Number 123878 by liberty last updated on 29/Nov/20

N i n e c h a i r s i n a r o w a r e t o b e o c c u p i e d b y

s i x s t u d e n t s a n d P r o f G e o r g e, P r o f P i e t e r,

a n d P r o f J o h n . T h e s e t h r e e p r o f e s s o r s a r r i v e

b e f o r e t h e s i x s t u d e n t s a n d d e c i d e t o c h o o s e

t h e i r c h a i r s s o t h a t e a c h p r o f e s s o r w i l l b e b e t w e e n

t w o s t u d e n t s . I n h o w m a n y w a y s c a n P r o f e s s o r G e o r g e

, P i e t e r a n d J o h n c h o o s e t h e i r c h a i r s ?

Answered by john_santu last updated on 29/Nov/20

l e t \oplus = p l a c e f o r 3 p r o f e s s o r

△ = p l a c e f o r s t u d e n t

△ △ \oplus △ △ \oplus △ △ \oplus △ △ \oplus △ △ \oplus

= P_{3}^{5} = \frac{5!}{2!} = 60 w a y s