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Irina18 [472]
2 years ago
7

A varsity boy's basketball team has ratio of seniors to juniors that is 7:4. The varsity girl's basketball team has a ratio of s

eniors to juniors that is 3 to 2. If each team has 12 juniors, which team has more seniors?
Mathematics
1 answer:
valentina_108 [34]2 years ago
4 0

Answer:

Girl's basketball team has more seniors

Step-by-step explanation:

A varsity boy's basketball team has ratio of seniors to juniors that is 7:4.

Let there are 7x seniors and 4x juniors in boy's basketball team.

ATQ,

7x+4x = 12

11x = 12

x = 12/11

Seniors = 7\times \dfrac{12}{11}=7.63

The varsity girl's basketball team has a ratio of seniors to juniors that is 3 to 2.

Let there are 7x seniors and 4x juniors in girl's basketball team.

3x+2x = 12

5x = 12

x = 12/5

Seniors = 7\times \dfrac{12}{5}=16.8

As we can see that girl's basketball team has more seniors as compared to the boy's team.

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Step-by-step explanation:

Number of females = 7

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^nC_r=\dfrac{n!}{r!(n-r)!}

(a)

Total ways of selecting 3 females and 2 males.

\text{Total ways}=^7C_3\times ^5C_2

\text{Total ways}=\dfrac{7!}{3!(7-3)!}\times \dfrac{5!}{2!(5-2)!}

\text{Total ways}=35\times 10

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Total ways of selecting 4 females and 1 male.

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\text{Total ways}=32\times 5

\text{Total ways}=175

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Total ways of selecting 5 females.

\text{Total ways}=^7C_5\times ^5C_0

\text{Total ways}=21\times 1

\text{Total ways}=21

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Total ways of selecting at least 4 females.

Total ways = 4 females + 5 females

\text{Total ways}=175+21

\text{Total ways}=196

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