Question:
An engineer is required to visit a factory for exactly four days during the first $15$ days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits to the factory can be made by the engineer during $1-15$ June $2021$ is _____
An engineer is required to visit a factory for exactly four days during the first $15$ days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits to the factory can be made by the engineer during $1-15$ June $2021$ is _____
Updated On: Apr 25, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 495
Solution and Explanation
We need to put 4 stick (identical) between 11 balls (identical) such that no 2 stick are together
\(^{12}C_4 = \frac{12 \times 11 \times 10 \times 9}{4 \times 3 \times 2 \times 1} = 495\)
Was this answer helpful?
0
0
Top Questions on permutations and combinations
- A mother was asked how many gifts she had in the bag. She replied that there were dolls but six, cars but six, and all books but six. How many gifts had she in all?
- Karnataka PGCET - 2025
- Quantitative Aptitude
- permutations and combinations
- A person needs to find the fastest two horses from 16 horses. Only a race of 4 horses can be conducted at a time. What is the minimum number of races to be conducted to determine the fastest two? (Assume that horses will not get tired at all and time cannot be measured)
- Karnataka PGCET - 2025
- Quantitative Aptitude
- permutations and combinations
- In a school, 120 boys have registered for a singles carrom tournament. Each match eliminates one player. How many matches are to be organized to determine the champion?
- Karnataka PGCET - 2025
- Quantitative Aptitude
- permutations and combinations
- In how many ways can a chairperson, a secretary, and a treasurer be chosen from a group of 10 people, if each person can hold only one position?
- AP PGECET - 2025
- Mathematics
- permutations and combinations
How many possible words can be created from the letters R, A, N, D (with repetition)?
- NATA - 2025
- Quantitative Aptitude
- permutations and combinations
View More Questions
Questions Asked in JEE Advanced exam
- A projectile is thrown at an angle of \(60^\circ\) with the horizontal. Initial speed is \(270\, \text{m/s}\). A linear drag force \(F = -CV\) acts on the body. Find the horizontal displacement till \(t = 2\) seconds. Given \(C = 0.1\, \text{s}^{-1}\).
- JEE Advanced - 2025
- Projectile motion
- A single slit diffraction experiment is performed to determine the slit width using the equation, $ \dfrac{b d}{D} = m \lambda $, where $ b $ is the slit width, $ D $ the shortest distance between the slit and the screen, $ d $ the distance between the $ m^{\text{th}} $ diffraction maximum and the central maximum, and $ \lambda $ is the wavelength. $ D $ and $ d $ are measured with scales of least count of 1 cm and 1 mm, respectively. The values of $ \lambda $ and $ m $ are known precisely to be $ 600 \, \text{nm} $ and 3, respectively. The absolute error (in $ \mu\text{m} $) in the value of $ b $ estimated using the diffraction maximum that occurs for $ m = 3 $ with $ d = 5 \, \text{mm} $ and $ D = 1 \, \text{m} $ is ___.
- JEE Advanced - 2025
- Error Propagation
- Let $$ \alpha = \frac{1}{\sin 60^\circ \sin 61^\circ} + \frac{1}{\sin 62^\circ \sin 63^\circ} + \cdots + \frac{1}{\sin 118^\circ \sin 119^\circ}. $$ Then the value of $$ \left( \frac{\csc 1^\circ}{\alpha} \right)^2 $$ is \rule{1cm}{0.15mm}.
- JEE Advanced - 2025
- Some Applications of Trigonometry
Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter $ D $ of a tube. The measured value of $ D $ is:
- JEE Advanced - 2025
- Units and measurement
- Let $ I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} $ and $ P = \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix} $. Let $ Q = \begin{pmatrix} x & y \\ z & 4 \end{pmatrix} $ for some non-zero real numbers $ x, y, z $, for which there is a $ 2 \times 2 $ matrix $ R $ with all entries being non-zero real numbers, such that $$ QR = RP $$ Then which of the following statements is (are) TRUE?
- JEE Advanced - 2025
- Matrices
View More Questions