A representative is to be selected from each of 3 departmentsin a small college.

Question

A representative is to be selected from each of 3 departmentsin a small college. There are 7 people in the first department, 5in the second department, and 4 in the third. a.) How many different groups of 3 representatives arepossible? Answer 140 b.) how many groups are possible if any number (at least 1) upto 3 representatives can form a group? (Each department is stillrestricted to at most one representative). Answer 239 I know the answers but have no idea how to get them...Pleasehelp! A representative is to be selected from each of 3 departmentsin a small college. There are 7 people in the first department, 5in the second department, and 4 in the third. a.) How many different groups of 3 representatives arepossible? Answer 140 b.) how many groups are possible if any number (at least 1) upto 3 representatives can form a group? (Each department is stillrestricted to at most one representative). Answer 239 I know the answers but have no idea how to get them...Pleasehelp! I know the answers but have no idea how to get them...Pleasehelp!

Explanation / Answer

7 First (F) , 5 Second (S) and 4 Third (T) people arethere.
a) # of different groups of 3 representatives possible = # ofchoosing 1 representative from 7 F * # of ways of choosing 1 from 5S * # of ways of choosing 1 from 4 Ts
= 7C1 * 5C1 * 4C1 =7*5*4 = 140
b) # of groups possible with 1member = # of ways of choosing 1person from any department. = choosing 1 from any (7+5+4 = 16) 16people = 16C1 = 16 ways.
# of groups possible with 2 members = # of groups possiblewith F,S + # of groups possible with F,T + # of groups possiblewith S, T
= 7*5 + 7*4 +5*4 = 35 + 28+ 20 = 83 ways
# of groups possible with 3 members is from part a = 140ways.
therefore putting all three together # of ways possible withat least 1 member and maximum of 1 from each department = 16+83+140= 239 ways.
Hope this helps. Feel free to ask for anyclarifications.

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