Question:
An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is :
An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is :
Updated On: Apr 24, 2025
- 72 (7!)
- 18 (7!)
- 40 (7!)
- 36 (7!)
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Eight digit no divisible by 9 i.e. sum of digits divisible by 9
(i) Total no formed by 1,2,3,4,5, 6,7,8 = 81
(ii) Total no formed by 0,2,3,4,5,6,7,9 = 7$\times$7!
(iii) Total no formed by 1,0,3,4,5,6,9,8 = 7$\times$7!
(iv) Total no formed by 1,2,0,4,5,9,7,8 = 7$\times$7!
(v) Total no formed by 1,2,3,0,5,6,7,8 = 7$\times$7!
8! + 28 $\times$ 7 !
= 36 $\times$ 7 !
(i) Total no formed by 1,2,3,4,5, 6,7,8 = 81
(ii) Total no formed by 0,2,3,4,5,6,7,9 = 7$\times$7!
(iii) Total no formed by 1,0,3,4,5,6,9,8 = 7$\times$7!
(iv) Total no formed by 1,2,0,4,5,9,7,8 = 7$\times$7!
(v) Total no formed by 1,2,3,0,5,6,7,8 = 7$\times$7!
8! + 28 $\times$ 7 !
= 36 $\times$ 7 !
Was this answer helpful?
0
0
Top Questions on permutations and combinations
- The number of ways 16 oranges distributed to 4 children, each gets at least one.
- JEE Main - 2026
- Mathematics
- permutations and combinations
The number of strictly increasing functions \(f\) from the set \(\{1, 2, 3, 4, 5, 6\}\) to the set \(\{1, 2, 3, ...., 9\}\) such that \(f(i)>i\) for \(1 \le i \le 6\), is equal to:
- JEE Main - 2026
- Mathematics
- permutations and combinations
- If all the letters of the word 'UDAYPUR' are arranged in all possible permutations and these permutations are listed in dictionary order, then the rank of the word 'UDAYPUR' is
- JEE Main - 2026
- Mathematics
- permutations and combinations
- Let A = \{-2, -1, 0, 1, 2, 3, 4\. Let R be a relation on A defined by xRy if and only if \(2x + y \le 2\). Let \(l\) be the number of elements in R. Let \(m\) and \(n\) be the minimum number of elements required to be added in R to make it reflexive and symmetric relations respectively. Then \(l + m + n\) is equal to :}
- JEE Main - 2026
- Mathematics
- permutations and combinations
- Let \( S=\{1,2,3,4,5,6,7,8,9\} \). Let \( x \) be the number of 9-digit numbers formed using the digits of the set \( S \) such that only one digit is repeated and it is repeated exactly twice. Let \( y \) be the number of 9-digit numbers formed using the digits of the set \( S \) such that only two digits are repeated and each of these is repeated exactly twice. Then:
- JEE Main - 2026
- Mathematics
- permutations and combinations
View More Questions
Questions Asked in JEE Main exam
If a random variable \( x \) has the probability distribution
then \( P(3<x \leq 6) \) is equal to- JEE Main - 2026
- Conditional Probability
- Two distinct numbers $a$ and $b$ are selected at random from $1, 2, 3, \ldots, 50$. The probability that their product $ab$ is divisible by $3$ is
- JEE Main - 2026
- Probability
- Consider a modified Bernoulli equation. \[ P + \frac{A}{Bt^2} + \rho g(h + Bt) + \frac{1}{2} \rho v^2 = \text{constant} \] If t has the dimension of time then the dimensions of A and B are_________ respectively.
- JEE Main - 2026
- Units, Dimensions and Measurements
- In an experiment the values of two spring constants were measured as \(k_1 = (10 \pm 0.2)\) N/m and \(k_2 = (20 \pm 0.3)\) N/m. If these springs are connected in parallel, then the percentage error in equivalent spring constant is:
- JEE Main - 2026
- Units, Dimensions and Measurements
An infinitely long straight wire carrying current $I$ is bent in a planar shape as shown in the diagram. The radius of the circular part is $r$. The magnetic field at the centre $O$ of the circular loop is :
- JEE Main - 2026
- Current electricity
View More Questions
Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.