Advertisements
Advertisements
Question
Determine the number of arrangements of letters of the word ALGORITHM if consonants are at even positions.
Solution
In the word ALGORITHM even positions are 4 and consonants are 6.
∴ number of arrangements in which 6 consonants occupy 4 even positions = 6P4
Now, the remaining 5 positions can be occupied by remaining 5 letters in 5P5 ways.
Hence, the total number of words in which consonants occupy even positions
= 6P4 × 5P5
= `(6!)/((6 - 4)!) × 5! ...[(""^"n""P"_"r" = ("n"!)/(("n" - "r")!)),(""^"n""P"_"r" = "n"!)]`
= `(6!)/(2!) × 5!`
= `(6 × 5 × 4 × 3 × 2!)/(2!) × 5!`
= 6 × 5 × 4 × 3 × (5 × 4 × 3 × 2 × 1)
= 360 × 120
= 43200
∴ 43200 words can be formed if the consonants are at even positions.
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?
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.
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.
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 is next to T.
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.
How many numbers can be formed using the digits 0, 1, 2, 3, 4, 5 without repetition so that the resulting numbers are between 100 and 1000?
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?
A code word is formed by two distinct English letters followed by two non-zero distinct digits. Find the number of such code words.
Find the number of ways in which 5 letters can be posted in 3 post boxes if any number of letters can be posted in a post box.
Find the number of ways of arranging letters of the word MATHEMATICAL. How many of these arrangements have all vowels together?
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 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 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 begin with S and end with T
Find the number of arrangements of the letters in the word SOLAPUR so that consonants and vowels are placed alternately
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
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 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
All the words that can be formed using alphabets A, H, L, U and R are written as in a dictionary (no alphabet is repeated). Rank of the word RAHUL is ______.
