Advertisements
Advertisements
प्रश्न
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
उत्तर
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, then
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
∴ Total number of ways in which numbers not divisible by 5 can be formed = 5 × 5! = 5 × 120 = 600
APPEARS IN
संबंधित प्रश्न
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed?
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 4-digit numbers that can be formed using the digits 1, 2, 4, 5, 6, 8 if digits can be repeated.
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.
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
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 Y and T are together
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 4-digit numbers that can be formed using the digits 1, 2, 4, 5, 6, 8 if digits can be repeated
How many numbers can be formed using the digits 0, 1, 2, 3, 4, 5 without repetition so that 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 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.
In how many ways can 5 different books be arranged on a shelf if 2 books are never together
