CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations
A firm has 9 employees. It wants to divide them into three teams of 3 each, the teams being unlabelled and identical in function (no team is distinguished). In how many ways can this be done?
The employees can be divided in 280 ways. Dividing 9 people into three labelled groups of 3 gives 9!/(3!3!3!) = 1680. Because the teams are indistinguishable, the same grouping is counted 3! = 6 times, so divide: 1680/6 = 280.
- A280Correct
- B1680
- C84
- D560
Explanation
Ordered division into three labelled groups = 9!/(3!·3!·3!) = 1680. Since the teams are indistinguishable, divide by 3! = 6: 1680/6 = 280. The value 1680 is wrong as it treats teams as labelled.
Did you get it right without looking?
One question tells you little. A timed set on Permutation and Combinations shows your real accuracy, how long you take and where you lose marks.
More Permutation and Combinations questions
- Five friends, Arun, Bala, Charu, Deepa and Esha, sit in a row for a photograph. If Arun and Bala must always sit next to each other, in how …
- How many diagonals does a polygon with 8 sides have?
- A Mumbai firm offers 4 different laptop models and 3 different bag designs. Each customer picks one laptop and one bag as a bundle. How many…
- Seven different books, of which 3 are on costing and 4 are on law, are arranged on a shelf. In how many ways can they be arranged so that al…
- How many 3-digit numbers can be formed from the digits 0, 1, 2, 3, 4 if repetition of digits is allowed?
- If nC2 = 45, what is the value of n?