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The scatter chart given below shows the number of boys on the Y-axis and the number of girls on the X-axis in three different classes 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%. Q51. The number of girls in class P is 40% of the number of girls in R. If a teacher wants to make two groups, A and B, from classes 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 selected, find the difference between the number of ways he can make such groups from each class.

1. 23460
2. 22350
3. 21350
4. 22560

Correct answer: 23460

Solution

The probability condition gives the number of girls in class R, and then the number of girls in class P is 40% of that. After finding boys in each class from the scatter chart, the required number of ways is computed using combinations: \(\binom{g}{2}\binom{b}{1}\) for each class. The difference between the two counts is 23460.

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