CA Foundation · Quantitative Aptitude · Permutations and Combinations
A project manager needs to select 3 engineers from a team of 8 engineers to work on a critical task. In how many ways can this selection be made?
The number of ways to select 3 engineers from 8 is C(8,3) = 56, calculated using the combination formula where order does not matter. Permutations (336) would be incorrect here because the selection order is irrelevant.
- A56Correct
- B336
- C512
- D24
Explanation
This is a combination problem since the order of selection does not matter. We use the formula C(n,r) = n! / (r!(n-r)!). Here C(8,3) = 8! / (3! × 5!) = (8 × 7 × 6) / (3 × 2 × 1) = 336 / 6 = 56. The distractor 336 results from calculating permutations P(8,3) instead of combinations.
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
- 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…
- If nP2 = 90, what is the value of n?
- A password must contain exactly 8 characters: a mix of digits (0–9) and uppercase English letters (A–Z). The first character must be a lette…
- A shopkeeper in Jaipur distributes 10 identical laddus among 3 children so that each child gets at least one laddu. In how many ways can thi…
- How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6 where no digit is repeated?
- How many distinct arrangements of the letters of the word COMMITTEE are there in which all the vowels stay together?