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The University of Ballygobackwards has three colleges:

the College of Science, which has 20 staff, 5 of whom are female;
the College of Engineering, which has 5 staff, 2 of whom are female;
and the College of Arts, which has 16 staff, 8 of whom are female.
Each college has a Dean, who is chosen from the staff in that college. What is the total number of ways these three Deans can be chosen?

Answer:

How many ways can three Deans be chosen, so that at least one of them is female?

Answer:

Respuesta :

Answer:

Step-by-step explanation:

given that the  University of Ballygobackwards has three colleges:

college      Science          Engineering                      Arts    

Males             15                        3                                8

Females           5                       2                                8

Total no of ways to choose 3 deans each for one college from staff

= [tex]20C1 (5C1)(16C1)\\= 1600[/tex]

b) Atleast one is a female

The ways to choose atleast one is a female = total ways - no female

=total ways -choosing only one male for each college

=[tex]1600-15C1(3C1)(8c1)\\=1600-360\\=1240[/tex]

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