Maths · Simple applications
There are 4 balls of different colours boxes of colours same as those of the bal
There are 4 balls of different colours \( \& 4 \) boxes of colours same as those of the balls. The number of ways in which the balls, one in each box, could be placed such that exactly no ball go to the box of its own colour is:
- A. 9
- B. 30
- C. 20
- D. None
Step-by-step solution
The number of ways to place 4 distinct balls into 4 distinct boxes such that no ball goes into the box of its own color is the number of derangements of 4 items. Derangement formula: D4 = 4! * (1 - 1/1! + 1/2! - 1/3! + 1/4!) = 24 * (1 - 1 + 1/2 - 1/6 + 1/24) = 24 * (9/24) = 9.
Related MCQs
- All the five digit numbers that can be formed using the digits 1,2,3,4,5 without repetition, are arranged in the decreasing order of magnitu…
- The total number of ways of formation of five letter words from the letters of the word is…
- Assertion In the shop there are five types of ice- creams available, a child buys six ice- creams. Reason The number of different ways the c…
- Given:…
- The number of words that can be formed out of the letters of the word "ARTICLE" so that the vowels occupy even places is…