Advertisements
Advertisements
Question
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
Advertisements
Solution
A number of 6 different digits is to be formed from the digits 3, 4, 5, 6, 7, 8 which can be done in 6P6 i.e., 6! = 720 ways
If the number is not divisible by 5
Unit’s place can be any digit from 3, 4, 6, 7, 8 which can be selected in 5 ways.
Other 5 digits can be arranged in 5P5
i.e., 5! ways
∴ Required number of numbers not divisible by 5
= 5 × 5!
= 5 × 120
= 600
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 not allowed?
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.
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 arrangements of the letters in the word BERMUDA so that consonants and vowels are in the same relative positions.
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?
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?
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
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 end in ST
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 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 ways in which 5 letters can be posted in 3 post boxes if any number of letters can be posted in a post box.
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
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
