a company has 13 employees, 8 of whom belong to the union. if 5 people work any one shift and the union contract specifies that at least 4 union members work each shift, then how many different combinations of employees might work any given shift ?
total employees =13
# of unions employees =8
# of non union employees = 13-8= 5
we can select 4 employees from union workers = 8C4 = 8!/(8-4)!*4!
and 1 from non-union worker = 5C1 = 5!/(5-1)!*1!
=> 8C4 * 5C1 = 350
but the Answer explanation says that i have to add 8C5
8C5= the number of ways to select 5 union workers
i.e { 8C4 * 5C1) + 8C5 = 406 answer
i don't understand why we have to add 8C5.
Thanks
Kaplan Combination Question
This topic has expert replies
-
- Legendary Member
- Posts: 1119
- Joined: Fri May 07, 2010 8:50 am
- Thanked: 29 times
- Followed by:3 members
because we have to select AT LEAST 4 employees from union workers thusnasir wrote:a company has 13 employees, 8 of whom belong to the union. if 5 people work any one shift and the union contract specifies that at least 4 union members work each shift, then how many different combinations of employees might work any given shift ?
total employees =13
# of unions employees =8
# of non union employees = 13-8= 5
we can select 4 employees from union workers = 8C4 = 8!/(8-4)!*4!
and 1 from non-union worker = 5C1 = 5!/(5-1)!*1!
=> 8C4 * 5C1 = 350
but the Answer explanation says that i have to add 8C5
8C5= the number of ways to select 5 union workers
i.e { 8C4 * 5C1) + 8C5 = 406 answer
i don't understand why we have to add 8C5.
Thanks
1/ we select 4 employees from uni and 1 empoyee who is not from union
2/ we select totally 5 people from union
( because of the word AT LEAST we have to get 8C5)
- Maciek
- Master | Next Rank: 500 Posts
- Posts: 164
- Joined: Sun Jul 18, 2010 5:26 am
- Thanked: 49 times
- Followed by:4 members
- GMAT Score:710
Nasir!
Your reasoning is correct.
8C5= the number of ways to select 5 union workers
The key word is 'at least'. Therefore, we need to add up combinations.
Either 4 union members work a shift or 5 union members work a shift.
Hence, we should add 8C5.
Hope it helps!
Best,
Maciek
Your reasoning is correct.
8C5= the number of ways to select 5 union workers
The key word is 'at least'. Therefore, we need to add up combinations.
Either 4 union members work a shift or 5 union members work a shift.
Hence, we should add 8C5.
Hope it helps!
Best,
Maciek
"There is no greater wealth in a nation than that of being made up of learned citizens." Pope John Paul II
if you have any questions, send me a private message!
should you find this post useful, please click on "thanks" button
if you have any questions, send me a private message!
should you find this post useful, please click on "thanks" button