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
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
