Question:
A five digit number divisible by $3$ is to be formed by using the numerals $0$, $1$, $2$, $3$, $4$ and $5$ without repetition. The total number of ways in which can be done is
A five digit number divisible by $3$ is to be formed by using the numerals $0$, $1$, $2$, $3$, $4$ and $5$ without repetition. The total number of ways in which can be done is
Updated On: Jun 14, 2022
- $216$
- $600$
- $240$
- $3125$
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Since, a five-digit number is formed using the digits $\{0,1,2,3,4$ and $5\}$ divisible by $3$ i.e. only possible when sum of the digits is multiple of three.
Case I Using digits $0, 1, 2, 4, 5$
Number of ways $= 4 \times 4 \times 3 \times 2 \times 1 = 96$
Case II Using digits $1, 2, 3, 4, 5 $
Number of ways $= 5 \times 4 \times 3 \times 2 \times 1 = 120$
$\therefore$ Total numbers formed $= 120 + 96 =216$
Case I Using digits $0, 1, 2, 4, 5$
Number of ways $= 4 \times 4 \times 3 \times 2 \times 1 = 96$
Case II Using digits $1, 2, 3, 4, 5 $
Number of ways $= 5 \times 4 \times 3 \times 2 \times 1 = 120$
$\therefore$ Total numbers formed $= 120 + 96 =216$
Was this answer helpful?
0
0
Top JEE Advanced Mathematics Questions
- In a $\triangle$ ABC w ith fixed base BC, the vertex A moves such that cos B + cos C = 4 $ sin^2 \frac{A}{2}$. If a, b and c denote th e lengths of th e sides of th e triangle opposite to the angles A, B and C respectively, then
- Let $P=[a_{ij}]$ be a $3\times3$ matrix and let $Q=[b_{ij}]$ where $b_{ij}=2^{i+j} a_{ij}$ for $1 \le i, j \le $.If the determinant of $P$ is $2$, then the determinant of the matrix $Q$ is
- For the equation $3x^2+px+3=0,p>0,$ if one of the root is square of the other, then p is equal to
- The equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$ has
Let \(f(x)=x+log_{e}x−xlog_{e}x,\text{ }x∈(0,∞)\).
- Column 1 contains information about zeros of \(f(x)\), \(f'(x)\) and \(f''(x)\).
- Column 2 contains information about the limiting behavior of \(f(x)\), \(f'(x)\) and \(f''(x)\) at infinity.
- Column 3 contains information about increasing/decreasing nature of \(f(x)\) and \(f'(x)\).
View More Questions
Top JEE Advanced permutations and combinations Questions
- The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN, is
- Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangements is
- If $r, s, t$ are prime numbers and p , q are the positive integers such th a t LCM of p , q is $r^2 s^4 t^2$ then the number of ordered pairs (p, q) is
- An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2,5 and 7. The smallest value of n for which this is possible, is
- The value of the expression \(^{47}C_4+ \displaystyle \sum^5_{j = 1} , ^{52-j}C_3\) is
View More Questions
Top JEE Advanced Questions
- Yellow light is used in a single slit diffraction experiment with slit width of 0.6 mm. If yellow light is replaced by X-rays, then the observed pattern will reveal
- The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image.
- A concave lens of glass, refractive index 1.5 has both surfaces of same radius of curvature R. On immersion in a medium of refractive index 1.75, it will behave as a
- The position vector $\vec{r}$ of a particle of mass $m$ is given by the following equation $\vec{r}(t)=\alpha t^{3} \hat{i}+\beta t^{2} \hat{j}$ where $\alpha=\frac{10}{3} \,ms ^{-3}, \beta=5\, ms ^{-2}$ and $m =0.1 \,kg$. At $t =1\, s$, which of the following statement (s) is (are) true about the particle?
- In an n-p-n transistor circuit, the collector current is 10 mA. If 90% of the electrons emitted reach the collector
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.