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A class consists of 45 students with the ratio of boys to girls in the 29 Jun 2020, 08:23
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45% (medium)

Question Stats:

76% (02:51) correct 24% (02:51) wrong based on 321 sessions

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A class consists of 45 students with the ratio of boys to girls in the class equal to 3:2. In a Science test, 40% of the class passed the test such that there were an equal number of boys and girls who passed the test. Find the number of ways in which 2 boys and 2 girls can be selected such that out of the selected boys and girls, exactly 1 boy and 1 girl failed the test?

A. 3*9^3
B. 2^2*9^3
C. 9^4
D. 2*9^4
E. 9^2*18^2
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D
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A class consists of 45 students with the ratio of boys to girls in the 29 Jun 2020, 09:26
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Kritisood
A class consists of 45 students with the ratio of boys to girls in the class equal to 3:2. In a Science test, 40% of the class passed the test such that there were an equal number of boys and girls who passed the test. Find the number of ways in which 2 boys and 2 girls can be selected such that out of the selected boys and girls, exactly 1 boy and 1 girl failed the test?

A. 3*9^3
B. 2^2*9^3
C. 9^4
D. 2*9^4
E. 9^2*18^2
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Number of boys and girls = 27 and 18
40% of 45 or 18 pass the test, out of which 9 are boys and 9 are girls.

Boys : 27, out of which 9 pass the test and 18 fail.
Ways to select one of each =9C1*18C1=9*18

Girls : 18, out of which 9 pass and 9 fail.
Ways to select one of each =9C1*9C1=9*9

Total ways =9*18*9*9=\(2*9^4\)

D
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A class consists of 45 students with the ratio of boys to girls in the 29 Jun 2020, 09:42
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Explanation:
Total Students = 45
Ratio: 3:2 (Boys to Girls)
B=27, G=18
40% pass the test = 45x0.4 = 18
Means 9 Boys & 9 Girls passed the test.
Boys (1 pass out 9, 1 fail out of 18) = 9C1 x 18C1 = 9x18 = 2x9x9
Girls (1 pass out 9, 1 fail out of 9) = 9C1 x 9C1 = 9x9
Total ways = 2x9x9x9x9
=2x9^4
IMO-D
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A class consists of 45 students with the ratio of boys to girls in the 11 Jul 2020, 01:13
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Kritisood
A class consists of 45 students with the ratio of boys to girls in the class equal to 3:2. In a Science test, 40% of the class passed the test such that there were an equal number of boys and girls who passed the test. Find the number of ways in which 2 boys and 2 girls can be selected such that out of the selected boys and girls, exactly 1 boy and 1 girl failed the test?

A. 3*9^3
B. 2^2*9^3
C. 9^4
D. 2*9^4
E. 9^2*18^2
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Total 45 students
boys to girls ratio in class=3:2

3x+2x=45
x=9
Therefore no. of boys=27 and no. of girls=18

Now, 40% of students passed the test= 45*(40/100)=18 students passed the test

As said no. of boys and girls passed in the test are equal, therefore 9boys and 9girls

Remaining boys who didn't pass=27-9=18 boys

Remaining girls who didn't pass=18-9= 9 girls

number of ways in which 1 boy selected who passed the test=9

number of ways in which 1 boy selected who failed the test=18

number of ways in which 1 girl selected who passed the test=9

number of ways in which 1 girl selected who failed the test=9

9*9*18*9=2*9^4

Answer D

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A class consists of 45 students with the ratio of boys to girls in the 31 Jul 2023, 22:32
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As per the given scenario

No. of boys = 27 (3*45/5=27)
No. of girls = 18 (2*45/5=18)

No. of students who passed = 40% of 45 = 18
Since no. boys and girls who pass the test are equal we can say that 9 boys and 9 girls pass the test

Therefore no. of boys who failed the test = 27-9=18
No. of girls who failed the test=18-9=9

Let,
a= no. ways of selecting a boy who passed the test
b= no. ways of selecting a boy who failed the test
c= no. ways of selecting a girl who passed the test
d= no. ways of selecting a girl who failed the test

the number of ways in which 2 boys and 2 girls can be selected such that out of the selected boys and girls, exactly 1 boy and 1 girl failed the test
=a*b*c*d
=(18C1)(9C1)(9C1)(9C1)
=18*9*9*9
=2*9^4

Hence D
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A class consists of 45 students with the ratio of boys to girls in the 08 Apr 2026, 07:06
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Deconstructing the Question

The class has \(45\) students with boys:girls ratio \(3:2\).

So the class has

\(27\)

boys and

\(18\)

girls.

Also, \(40\%\) of the class passed:

\(0.4 \cdot 45 = 18\)

Since an equal number of boys and girls passed, we have

\(9\)

boys passed and

\(9\)

girls passed.

Therefore,

\(27 - 9 = 18\)

boys failed, and

\(18 - 9 = 9\)

girls failed.

We must choose \(2\) boys and \(2\) girls such that exactly \(1\) boy and \(1\) girl failed.

Step-by-step

Choose the boys:

We need \(1\) boy who passed and \(1\) boy who failed.

\(\binom{9}{1}\binom{18}{1} = 9 \cdot 18\)

Choose the girls:

We need \(1\) girl who passed and \(1\) girl who failed.

\(\binom{9}{1}\binom{9}{1} = 9 \cdot 9\)

Multiply:

\((9 \cdot 18)(9 \cdot 9) = 18 \cdot 9^3\)

Rewrite:

\(18 \cdot 9^3 = 2 \cdot 9^4\)

Answer D
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