Question

A five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

Solution

Correct option is

216

The sum of the numerals 0, 1, 2, 3, 4 and 5 is 15. We know that five digit is divisible by 3 if and only if the sum of its digits is divisible by 3. Therefore, we should not eight 0 or 3 while forming the five digit numbers. If we do not user 0, then the remaining digit can be arranged in  ways. If we do not use 3, then the remaining digit can be

 ways to obtain a five digit number. Thus, the total number of such 5 digit numbers is 120 + 96 = 216.

SIMILAR QUESTIONS

Q1

The number of five digit telephone numbers having at least one of their digits repeated is

Q2

Let P be a prime number such that P  23. Let n = p! + 1. The number of primes in the list n + 1, n + 2, n + 3, … n + p – 1 is

Q3

The term digit of 1! + 2! + 3! + … + 49! Is

Q4

Four dice are rolled. The number of possible outcomes in which least one die shows 2 is

Q5

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen. The number of ways of choosing P and Q so that P  Q = Ï• is

Q6

Let E = {1, 2, 3, 4} and F = {ab}. then the number of onto functions from E to F is

Q7

The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is

Q8

The range of function 

Q9

The number of ways of arranging letters of the word RACHIT so that the vowels are in alphabetical order is

Q10

The number of ways in which a mixed double game can be arranged from amongst 9 married couple if no husband and wife play in the same game is