Question
Find the number of ways to arrange each letter of the
word 'EDUCATIONAL' such that all the vowels always come together.Solution
Number of letters = 11
Take all the vowels (EUIOAA) as one entity.
Number of letters now = 5 + 1 = 6!
Number of ways to arrange all the letters = 6! = 720
Number of ways to arrange vowels = 6! Ă· 2! = 720 Ă· 2 = 360
Required number of ways = 720 Ă— 360 = 2,59,200
Using all the letters of the word RELIAN, how many words start with a vowel but end with a consonant?
Find total number of ways in which the word “ACCOMMODATE” can be arranged.
- A group consists of 9 boys and 8 girls. In how many ways can 3 boys and 5 girls be selected from the group?
From the digits 1, 2, 3, 4, 5, 6 and 7, how many 4‑digit even numbers can be formed without repetition?
In how many different ways can the letters of the word “INCORPORATION” be arranged so that the vowels comes together?
In how many different ways can the letter of the word CHESTNUT is arranged so that vowels always occur together?
In a bag there are 4 red balls, 3 green balls, and 5 blue balls. If one ball is drawn at random from the bag, what is the probability of drawing a green...
- Six people out of which 3 are brothers and the rest are strangers are to be seated in a row. Find the number of ways in which all three brothers are not si...
How many arrangements of the word COMMITTEE are possible if the vowels are always together?
A team of 7 researchers is to be formed from 6 biologists and 4 chemists. Find the number of ways to form the team if it must include at least 5 biologi...
Relevant for Exams:
