SOLUTION: A company has hired 10 new employees, 7 men and 3 women. The company must assign 5 of them to the morning shift, 3 of them to the swing shift, and the rest of them to the graveyard

Algebra ->  Probability-and-statistics -> SOLUTION: A company has hired 10 new employees, 7 men and 3 women. The company must assign 5 of them to the morning shift, 3 of them to the swing shift, and the rest of them to the graveyard      Log On


   

Question 1155894: A company has hired 10 new employees, 7 men and 3 women. The company must assign 5 of them to the morning shift, 3 of them to the swing shift, and the rest of them to the graveyard shift.
Find the probability that at least one man is assigned to the swing shift?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The complement event of "at least one man is assigned to the swing shift" is
the event that all 3 women are assigned to the swing shift.
That's 

  the number of ways to have all 3 women on the swing shift      1       1
------------------------------------------------------------- = ---- = -----
the number of ways to have any 3 of the 10 on the swing shift   10C3    120

So 1/120 is the probability that all 3 women will be on the swing shift.

Therefore 1 - 1/120 or 119/120 is the probability that there will be at least
one man on the swing shift.

[It doesn't matter about the other two shifts.  We can ignore them. We are
considering each of the 10 people either to be assigned to the swing shift or
elsewhere.]

Edwin