Mathematics: 11. jillian needs to make a group of 5 people. she has 10 democrats, 13 republicans, and 7 independents to choose from. (a) what is the probability that the group of 5 people will have 2 democrats, 2 republicans, and 1 independent

11. jillian needs to make a group of 5 people. - id1153995852, austintules2005

janeou17xn

11.01.2022

0.1724 or 17.24%

Step-by-step explanation:

There are

10+13+7 = 30 people

so there are C(30,5) combinations of 30 elements taken 5 at a time ways to select groups of 5 people.

$C(30,5)=\displaystyle\binom{30}{5}=\frac{30!}{5!25!}=142,506$

There are C(10,2) combinations of 10 elements taken 2 at a time ways to select the 2 Democrats

$C(10,2)=\displaystyle\binom{10}{2}=\frac{10!}{2!8!}=45$

There are C(13,2) combinations of 13 elements taken 2 at a time ways to select the 2 Republicans

$C(13,2)=\displaystyle\binom{13}{2}=\frac{13!}{2!11!}=78$

There are C(7,1) combinations of 7 elements taken 1 at a time ways to select the Independent

$C(7,1)=\displaystyle\binom{7}{1}=\frac{7!}{1!6!}=7$

By the Fundamental Principle of Counting, there are

45*78*7 = 24,570

ways of making the group of 5 people with 2 Democrats, 2 Republicans and 1 independent, and the probability of forming the group is

$\displaystyle\frac{24,570}{142,506}=0.1724$ or 17.24%

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natem725

25.09.2021

answer:

Leroy has 60, Sean has 10

Step-by-step explanation:

Leroy=6x

Sean=x

6x+x=7x

7x=70

Divide by 7 on both sides:

x=10

Sean has 10

Leroy=6(10)

Leroy has 60

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