The letters of the word 'JOURNEY' 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.
From a group of 4 men and 6 women, in how many ways can 3 men and 2 women or 2 men and 3 women be selected?
How many words can be formed with 7 distinct consonants and 4 distinct vowels such that vowels stay together at the end of each word?
How many 4 digit numbers can be formed with a given set of 7 distinct digits?
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 007" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-08