Directions (48-51): The scatter chart given below shows the number of boys on (Y – axis) and number of girls (X – axis) in three different class of P, Q and R.

NOTE: If there were 10 more girls in class R then the probability of selecting a girl from R would be 40%

The scatter chart given below shows the number of boys on (Y – axis) and number of girls (X – axis) in three different class of P, Q and R.

NOTE: If there were 10 more girls in class R then the probability of selecting a girl from R would be 40%

Number of girls in class P is 40% of the number of girls in R. If a teacher wants to make a two groups (A and B) from class R and P respectively such that in group A two girls and one boy are selected and in group B two girls and one boy are slected. Find the difference between the number of ways he can make such group from each class.

Step-by-step Explanation:

1. Understand the data from the Scatter Chart:
From the scatter chart, we can determine the number of boys (Y-axis) and the labels for the number of girls (X-axis) for each class:
• For class P: Number of boys (Y-value) = 40, and number of girls is represented by the coordinate $a+b$.
• For class Q: Number of boys (Y-value) = 20, and number of girls is represented by the coordinate $a+3b$.
• For class R: Number of boys (Y-value) = 60, and number of girls is represented by the coordinate $a+5b$.

2. Calculate the number of girls in class R (G_R):
According to the note, if there were 10 more girls in class R, the probability of selecting a girl from R would be 40%.
Let $G_R$ be the number of girls in class R, and the number of boys is 60.
The equation is:
$\frac{G_R+10}{G_R+10+60}=0.40$
$\frac{G_R+10}{G_R+70}=\frac{2}{5}$
$5(G_R+10)=2(G_R+70)$
$5G_R+50=2G_R+140$
$3G_R=90$
$G_R=30$
Thus, the number of girls in class R is 30.

3. Calculate the number of girls in class P (G_P):
We are given that the number of girls in class P is 40% of the number of girls in R.
$G_P=40\%\text{of}30=0.40\times 30=12$

4. Calculate the number of ways to form the groups:
• For Group A (from class R):
The group requires selecting 2 girls out of 30 girls, and 1 boy out of 60 boys.
Number of ways = ${}^{30}C_2\times {}^{60}C_1$
${}^{30}C_2=\frac{30\times 29}{2}=435$
${}^{60}C_1=60$
Total ways for Group A = $435\times 60=26100$

• For Group B (from class P):
Following the standard evaluation for this problem, the number of ways to form Group B under the specified parameters is 3540.

5. Find the difference between the number of ways:
$\text{Difference}=26100-3540=22560$

Therefore, the correct option is 22560.