CA Foundation · Quantitative Aptitude · Permutations and Combinations
A Mumbai trader has to display 4 identical red files, 3 identical blue files and 2 identical green files in a row on a shelf. In how many distinct colour patterns can this be done?
The answer is 1260. Nine files are arranged in a row, with 4 identical red, 3 identical blue and 2 identical green, so the patterns number 9!/(4!·3!·2!) = 362880/288 = 1260.
- A1260Correct
- B362880
- C2520
- D630
Explanation
There are 9 files with repetitions 4, 3 and 2. Number of patterns = 9!/(4!·3!·2!) = 362880/(24·6·2) = 362880/288 = 1260. The value 362880 ignores identical files.
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