CA Foundation · Quantitative Aptitude · Permutations and Combinations
From a group of 9 people, a committee of 4 is to be formed. Two of the 9, Rohan and Sneha, refuse to serve together on the committee. In how many ways can the committee be formed?
There are 105 possible committees. Total selections of 4 from 9 are 126. Those that include both Rohan and Sneha number 21, as the other two members come from the remaining 7. Subtracting 21 from 126 leaves 105 committees.
- A126
- B91
- C105Correct
- D35
Explanation
Total = 9C4 = 126. Committees containing both Rohan and Sneha: choose the other 2 from the remaining 7 = 7C2 = 21. Valid committees = 126 - 21 = 105. The value 91 wrongly subtracts 35.
Did you get it right without looking?
One question tells you little. A timed set on Permutations and Combinations shows your real accuracy, how long you take and where you lose marks.
More Permutations and Combinations questions
- The value of 10C3 + 10C4 equals which of the following?
- A student must choose 2 optional subjects from 6 available subjects. In how many ways can the choice be made?
- How many 4-digit numbers greater than 5000 can be formed using the digits 0, 3, 5, 6, 8, 9 if digits may be repeated?
- A surveyor marks 10 points on a plot map, of which exactly 4 lie on one straight line and no other three are collinear. How many triangles c…
- Eight members of a family, including a married couple Mr. and Mrs. Iyer, sit around a circular table. In how many ways can they be seated so…
- How many distinct 6-digit numbers can be formed using all the digits 1, 1, 2, 2, 3, 3 (each digit used exactly the number of times given)?