Multiple choice

Passage

Directions: Read the following information carefully to answer the question that follows: MARKS OBTAINED BY A CLASS OF 46 STUDENTS IN A TEST OUT OF 100 Number of Children Marks 4 <10 12 <20 21 <30 28 <40 36 <50 42 <60 46 <70 (Assume each student got integral marks)

In how many ways 3 students chosen at random from the class have y marks, where 30 ≤ y < 60?

  1. 1771

  2. 1540

  3. 1330

  4. 1140
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number of students with marks y where 30 <= y < 60 corresponds to the range 30 to 60. From the table: students < 40 is 28, < 50 is 36, < 60 is 42. So, students in [30, 40) is 28-21=7, [40, 50) is 36-28=8, [50, 60) is 42-36=6. Total students = 7+8+6 = 21. Ways to choose 3 = 21C3 = (21*20*19)/(3*2*1) = 7*10*19 = 1330.

AI explanation

We first determine the number of students who scored between 30 and 59 by using the cumulative frequencies provided. The number of students who scored at least 30 but less than 60 is 46 minus 28, which gives us 18 students. We must select 3 students from this specific group of 18 eligible students. Using the combination formula nCr = n! / (r!(n-r)!), we calculate 18C3 as (18 * 17 * 16) / (3 * 2 * 1), which results in 1330 ways.

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