What is the value of 7C2?
The letters of the word 'PERIOD' have to be arranged such that the vowels occupy only the odd positions. How many different ways are possible?
This word has 6 letters, out of which 3 are consonants and 3 are vowels. The vowels have to occupy three fixed odd positions. We can place 3 vowels in first odd place, 2 in second odd place and 1 in the third odd place, giving 3 × 2 × 1 = 6 permutations. This will be done with the consonants also. So the total possibilities are 6 × 6 = 36.
In how many ways can 3 letter words be formed by using a given set of 6 consonants?
The letters of the word 'HOLIDAY' have to be arranged such that the vowels come together. How many different ways are possible?
This word has 7 letters, out of which 4 are consonants and 3 are vowels. The vowels have to occupy three contiguous positions. This triad can be arranged in 3! ways like this: we can place 3 vowels in first place, 2 in second place and 1 in the third place, giving 3 × 2 × 1 = 6 permutations. Next, we have to arrange the 4 consonants and the triad treated as one letter, giving 5! = 120 possibilities. So the total possibilities are 6 × 120 = 720.
In how many ways can 4 prizes be given to 3 students if each of them is equally eligible?
This Blog Post/Article "Permutations and Combinations Quiz Set 011" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-10-26.