Question

the intergalactic council has 30 members; there are 13 Balin, 11 Calin, and 6 Daylist.

They want to pick 5 council members to study the possibility of inducting the Macklarks, into the intergalactic council

This group will have a team leader and 2nd in-charge, and 3 team members

a) how many ways can the 5 council members be picked

b) how many ways can they pick the 5 council members, if the leader and 2nd in-charge, first then pick the 3 team members

c) how many ways can they pick the 5 council members, then choose the the leader and 2nd in-charge out of the 5 picked

d) how many ways can they pick 5 Balins

e) how many ways can they pick 2 Daylist

Answer 1

a) Number of ways to pick 5 team members is computed here as:

= Number of ways to choose 5 members from total 30 member council

b) Number of ways to pick 5 council members if the meader and 2nd in charge are picked first and then the three team members is computed here as:

= Number of ways to pick a leader from 30 members * Number of ways to pick a 2nd in charge from remaining 29 members * Number of ways to pick the remaining 3 members from 28 members left

c) Number of ways to first pick 5 member and then choose leader and 2nd in charge is computed here as:

= Number of ways to pick 5 members from 30 members * Number of ways to select leader from 5 members picked * Number of ways to choose the 2nd in charge from remaining 4 members

d) Number of ways that 5 balins are picked is computed here as:

= Number of ways to choose 5 balins from 13 balins

e) Number of ways to pick 2 daylists is computed here as:

Number of ways to pick 2 daylist from 6 daylists