Question

There are $40$ doctors in a surgical department. In how many ways can they be arranged to form the following teams: (a) a surgeon and an assistant; (b) a surgeon and four assistants?

Answer 1

a) first divide the doctors into 20 groups with 2 persons in each and then select one as a surgeon this can be done $40!/20$and other as an assistant, this can be done in $2$ ways

$\therefore$ total number of ways is $40!/10$

b) ) first divide the doctors into 8 groups with 5 persons in each and then select one as a surgeon this can be done $40!/8$and others as assistants, this can be done in $5$ ways

$\therefore$ total number of ways is $5\times 40!/8!$