Answer
Verified
105.3k+ views
Hint: For finding the number of numbers divisible by 3 we use the permutation concept. First, we must know the divisibility rule of 3 which states that a number is divisible by 3 only when the sum of individual digits is divisible by 3. By using this we can easily solve our problem.
Complete step-by-step answer:
According to our problem, even digits can be stated as 0, 2, 4, 6, 8.
As the divisibility rule of 3 states that a number is divisible by 3 only when the sum of individual digits is divisible by 3. So, the 4 different even digit numbers are divisible by 3 = set of (2, 4, 6, 0) and (8, 6, 4, 0).
So, the number of combinations possible = $4!$.
But, if 0 occurs at first place then the number is not four digits. So, cases for 0 at first place = $3!$.
So, total valid combinations = $4!-3!=18$.
But there are two possible sets, so multiplying the obtained result by 2 we get total valid combinations as = $18\times 2=36$.
Therefore, option (b) is correct.
Note: The key concept of solving this problem is the knowledge of permutations and divisibility rule for 3. Once the total number of cases are obtained by using the given criteria, then by using permutation the final result can be evaluated without any error.
Complete step-by-step answer:
According to our problem, even digits can be stated as 0, 2, 4, 6, 8.
As the divisibility rule of 3 states that a number is divisible by 3 only when the sum of individual digits is divisible by 3. So, the 4 different even digit numbers are divisible by 3 = set of (2, 4, 6, 0) and (8, 6, 4, 0).
So, the number of combinations possible = $4!$.
But, if 0 occurs at first place then the number is not four digits. So, cases for 0 at first place = $3!$.
So, total valid combinations = $4!-3!=18$.
But there are two possible sets, so multiplying the obtained result by 2 we get total valid combinations as = $18\times 2=36$.
Therefore, option (b) is correct.
Note: The key concept of solving this problem is the knowledge of permutations and divisibility rule for 3. Once the total number of cases are obtained by using the given criteria, then by using permutation the final result can be evaluated without any error.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
Write an article on the need and importance of sports class 10 english JEE_Main
Name the scale on which the destructive energy of an class 11 physics JEE_Main
Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main
Choose the one which best expresses the meaning of class 9 english JEE_Main