Advertisements
Advertisements
Question
Determine the number of arrangements of letters of the word ALGORITHM if no two vowels are together.
Solution
There are 6 consonants in the word ALGORITHM.
They can be arranged among themselves in 6P6 i.e., 6! ways.
Let consonants be denoted by C.
_ C _ C _ C _ C _ C _ C _
There are 7 places marked by “______” in which 3 vowels are to be arranged.
∴ Vowels can be arranged in 7P3
= `(7!)/((7-3)!)`
= `(7xx6xx5xx4!)/(4!)`
= 210 ways
∴ Required number of arrangements
= 6! × 210 = 720 × 210 = 151200
∴ 151200 words can be formed if no two vowels are together.
APPEARS IN
RELATED QUESTIONS
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are allowed?
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed?
Determine the number of arrangements of letters of the word ALGORITHM if vowels are always together.
Determine the number of arrangements of letters of the word ALGORITHM if no two vowels are together.
In a group photograph, 6 teachers are in the first row and 18 students are in the second row. There are 12 boys and 6 girls among the students. If the middle position is reserved for the principal and if no two girls are together, find the number of arrangements.
Find the number of ways letters of the word HISTORY can be arranged if Y and T are together.
Find the number of ways letters of the word HISTORY can be arranged if Y is next to T.
Find the number of arrangements of the letters in the word BERMUDA so that consonants and vowels are in the same relative positions.
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 4, 5, 6, 8 if digits can be repeated.
Find the number of 6-digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition. How many of these numbers are divisible by 5?
A code word is formed by two distinct English letters followed by two non-zero distinct digits. Find the number of such code words.
A code word is formed by two distinct English letters followed by two non-zero distinct digits. Find the number of such code words that end with an even digit.
How many 4 letter words can be formed using letters in the word MADHURI if letters can be repeated
Determine the number of arrangements of letters of the word ALGORITHM if consonants are at even positions.
Determine the number of arrangements of letters of the word ALGORITHM if O is the first and T is the last letter
Find the number of ways so that letters of the word HISTORY can be arranged as Y and T are together
Find the number of ways so that letters of the word HISTORY can be arranged as Y is next to T
Find the number of ways so that letters of the word HISTORY can be arranged as there is no restriction
Find the number of ways so that letters of the word HISTORY can be arranged as begin and end with vowel
Find the number of ways so that letters of the word HISTORY can be arranged as end in ST
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 4, 5, 6, 8 if digits can be repeated
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 4, 5, 6, 8 if digits cannot be repeated
Find the number of 6-digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition. How many of these numbers are divisible by 5
Find the number of 6-digit numbers using the digits 3, 4, 5, 6, 7, 8 without repetition. How many of these numbers are not divisible by 5
In how many ways can 5 different books be arranged on a shelf if there are no restrictions
In how many ways can 5 different books be arranged on a shelf if 2 books are always together
In how many ways can 5 different books be arranged on a shelf if 2 books are never together
3 boys and 3 girls are to sit in a row. How many ways can this be done if there are no restrictions
3 boys and 3 girls are to sit in a row. How many ways can this be done if there is a girl at each end
3 boys and 3 girls are to sit in a row. How many ways can this be done if boys and girls are at alternate places
3 boys and 3 girls are to sit in a row. How many ways can this be done if all boys sit together
