From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?

Explanation

`:'` Total persons in committee = 8
`:.` No. of ways of choosing a chairman from 8 persons `= .^(8)P_(1)`
`= (lfloor8)/(ul(8-1)) =(lfloor8)/(lfloor7) = (8xx lfloor7)/(lfloor7) = 8`
Now, no of ways of choosing a vice-chairman from remaining 7 persons `=.^(7)P_(1)`
`= (lfloor7)/(ul(7-1)) = (lfloor7)/(lfloor6) = (7 xx lfloor6)/(lfloor6) = 7`
Therefore, total no. of ways of choosing a chairman and a vice-chairman `= .^(8)P_(1) xx .^(7)P_(1) = 8 xx 7 = 56`.