I keep getting the wrong answer for this, do any of you know how to do it?

Question

For this problem, assume 10 males audition, one of them being Winston, 7 females audition, one of them being Margaret, and 5 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available.

How many different ways can these roles be filled if exactly one of Winston and Margaret gets a part?

Answer 1

You begin considering two groups possible:

A1... groups with Winston
A2... groups with Margaret ... these sets are disjoint.

Evaluating the number of elements in set A1

Choose 2 males from 9 because Winston was already chosen
C(9,2)=9!/(2!7!)
Choose 1 female from 6 because Margareth must be out
C(6,1) = 6
Choose 2 children from 5
C(5,2) = 5!/(2!3!)
Now use the product rule: C(9,2).C(6,1).C(5,2)

Evaluating the number of elements in set A2

Choose 3 males from 9 because Winston must be out
C(9,3)
Choose 0 female from 6, because Margareth is already chosen
C(6,0)=1
Choose 2 children from 5
C(5,2)
Now use the product rule: C(9,3).C(6,0).C(5,2)

As the set A1 e A2 are disjoint you use the Addition rule

Total number is |A1| + |A2|

Answer 2

3*(9 comb 2)*(5 comb 2)= 1080. There are three different roles Winston can get and 9 comb 2 ways the remaining two roles can be divided up between the remaining 9 males. There are 5 comb 2 ways the baby roles can be determined and only 1 way the female role can be done since it goes to Margaret.

Answer 3

if both winston and margaret get a part, that means there are 9 males going for 2 roles, no more female roles, and the 5 kids for 2 roles. there are 36 ways to divide the male roles and 9 ways to divide the kids' roles. 36x9=324...i think

Answer 4

What is left to choose? Multiply your choices left for each part.

You need 2 more men and you have 9 to choose from. That sounds like 9 choose 2 or
9 * 8 /(2 * 1) = 36

You have 0 left to choose from the women. By definition, 0 choose 0 is 1.

You have 2 children to cast out of 5. That is 5 choose 2 or
5 * 4 /(2 * 1) = 10.

36 * 1 * 10 = 360 different ways to finish casting the show.

Answer 5

it is simple.(if wintson is selected)
1 winston so 2 other males in 10C2 or 45 ways
they can be in 6 permutations so 45*6 = 270 ways
the female canot be margaret so 6 ways
2 children in 5*4 ways = 20ways(permuation as AB and BA are different ways)
so number of ways = 270*6*20 = 270*120
if Winston is not selected then 9*8*7 ways = 504
one way female
20 ways children
so number of ways = 504*20
so total number of ways = 270*120+504*20

Answer 6

Since one male has been chosen then we have to chose two out of the rest nine. There was only one female role which has been chosen and nothing role has been left out of the six females. Two child is chosen out of five child. therefore all the ways will be as under.
9C2x6C0x5C2=36x1x10=360

Answer 7

Number of males: 10 - 1 = 9.
Number of combinations of two males: nCr = 36.

No more Females needed (because Margaret was picked).

Number of Children: 5.
Number of combinations of two children: nCr = 10.

Each combination of the Males can match up with each combination of the children.

Total number of combinations: No. of Males * No. of Children.
Total number of combinations: 36 * 10
Total number of combinations: 360 combinations.

Answer 8

360

For sure. I counted :-)

And, why such confusion wit 7 women, when there is only one Margaret and only one female role?

Answer 9

my dog is called winston and the pig is margaret but they have both been done so do they qualify ??

Answer 10

QWinston is dead and I don't know about thatcher