Choosing from three colours — Aptitude Question
Choosing from three colours: A bag has 6 red, 4 white and 5 blue balls. In how many ways can 3 balls of different… Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
A bag has 6 red, 4 white and 5 blue balls. In how many ways can 3 balls of different colours be drawn?
Options
- 60
- 90
- 120
- 150
Show the answer and the worked solution
Correct answer: C. 120
Worked solution
- One red from 6, one white from 4 and one blue from 5.
- Total = 6 × 4 × 5 = 120.
Answer: 120.
The idea
Independent selections multiply. Because exactly one is taken from each group, no combination formula is needed.
Shortcut. Three balls of different colours with only three colours means one of each, so no C(15,3) is needed: 4 × 5 = 20, then 20 × 6 = 120.
Common trap. Dividing 6 × 4 × 5 by 3! to 'remove the order' gives 20; the colours already label the three picks — one red, one white, one blue — so no selection is counted twice and the product needs no division.
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