Question

A committee of 3 students is to be formed from Arts and commerce course. Number of students in arts and commerce course is 12 and 16.The number of possible ways of a committee from the commerce course is what percent of the number of possible ways of committee contains 3 students  from the Arts course.
1. 123.45 %
2. 134.56 %
3. 254.54 %
4. 132.56 %
5. 109.90 %

Answer 1

Correct Answer - Option 3 : 254.54 %

Given

Number of students in commerce course = 16

Number of students in arts course = 12

Calculation:

Possible ways of forming committee from Arts course = ¹²C₃

= 12  × 11  × 10  × 9!/3  × 2  × 1  ×  9!

= 220

Possible ways of forming committee from commerce course = ¹⁶C₃

= 16  × 15  × 14  × 13!/ 3  × 2 × 1  × 13!

= 560

Required percentage = (560/220) × 100

= 254.54 %