The letters of the word 'TUESDAY' 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 a secretary and general secretary be chosen from a committee of 19 members?
How many four letter words, with all the letters different, can be formed out of the letters of the word 'BLACKSMITH'?
In how many ways can 9 different types of ice-creams be distributed among 5 boys?
The letters of the word 'MEXICO' 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.
This Blog Post/Article "Permutations and Combinations Quiz Set 008" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.