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.
From a group of 9 boys and 6 girls, in how many ways can 2 boys and 2 girls be selected?
2 men are standing in front of 3 cabins. In how many ways can they enter the cabins?
What is the value of 8P2?
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?
This Blog Post/Article "Permutations and Combinations Quiz Set 020" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-05-17.