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 divisible by 5
Advertisements
Solution
There are 6 different digits and we have to form 6-digit numbers, i.e., n = 6, r = 6
If no digit is repeated, the total numbers with 6-digits can be formed = nPr
= 6P6
= 6!
= 6 x 5 x 4 x 3 x 2 x 1
= 720.
Since the number is divisible by 5, the unit's place of 6-digits number can be filled in only one way by the digit 5.
Remaining 5 positions can be filled from the remaining 5 digits in 5P5 ways.
Hence, the total number of 6-digit numbers divisible by 5 = 1 x 5P5 = 5!
= 5 x 4 x 3 x 2 x 1
= 120.
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 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 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 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 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?
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.
Find the number of ways so that letters of the word HISTORY can be arranged as there is no restriction
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
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
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 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 all boys sit together
