Question:
The number of 4 digit numbers without repetition that can be formed using the digits 1, 2, 3, 4, 5, 6, 7 in which each number has two odd digits and two even digits is
The number of 4 digit numbers without repetition that can be formed using the digits 1, 2, 3, 4, 5, 6, 7 in which each number has two odd digits and two even digits is
Updated On: Apr 14, 2024
- 450
- 432
- 454
- 436
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Given digits are 1, 2, 3, 4, 5, 6, 7.
Two even digits can be selected in $^{3}C_{2}$
Two odd digits can be selected in $^{4}C_{2}$ ways.
These selected 4 digits can be arranged in 4! ways.
$\therefore\, Total \,number\, of \,ways=^{4}C_{2}. ^{3}C_{2}. 4!$
$=6\times3\times24$
$=18\times24$
$=432$
Two even digits can be selected in $^{3}C_{2}$
Two odd digits can be selected in $^{4}C_{2}$ ways.
These selected 4 digits can be arranged in 4! ways.
$\therefore\, Total \,number\, of \,ways=^{4}C_{2}. ^{3}C_{2}. 4!$
$=6\times3\times24$
$=18\times24$
$=432$
Was this answer helpful?
0
0
Top Questions on permutations and combinations
- How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?
- BITSAT - 2025
- Mathematics
- permutations and combinations
- If the number of seven-digit numbers, such that the sum of their digits is even, is $ m \cdot n \cdot 10^a $; $ m, n \in \{1, 2, 3, ..., 9\} $, then $ m + n $ is equal to
- JEE Main - 2025
- Mathematics
- permutations and combinations
- There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.
- MHT CET - 2025
- Mathematics
- permutations and combinations
Match List-I with List-II
List-I List-II (A) \(^{8}P_{3} - ^{10}C_{3}\) (I) 6 (B) \(^{8}P_{5}\) (II) 21 (C) \(^{n}P_{4} = 360,\) then find \(n\). (III) 216 (D) \(^{n}C_{2} = 210,\) find \(n\). (IV) 6720
Choose the correct answer from the options given below:- CUET (UG) - 2025
- General Aptitude
- permutations and combinations
- The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:
- JEE Main - 2025
- Mathematics
- permutations and combinations
View More Questions
Questions Asked in KCET exam
- If the number of terms in the binomial expansion of \((2x + 3)^n\) is 22, then the value of \(n\) is:
- KCET - 2025
- Binomial theorem
- A particle is in uniform circular motion. The equation of its trajectory is given by \( x = 2t^2 - 3t + 5 \), where \( x \) and \( y \) are in meters. The speed of the particle is 2 m/s. When the particle attains the lowest \( y \)-coordinate, the acceleration of the particle is (in \( \text{m/s}^2 \)):
- KCET - 2025
- Friction
- If \( A \) is a square matrix of order \( 3 \times 3 \), \( \det A = 3 \), then the value of \( \det(3A^{-1}) \) is:
- KCET - 2025
- Matrices
- A potential at a point A is 3 V and that at another point B is 5 V. What is the work done in carrying a charge of 5 mC from B to A?
- KCET - 2025
- Electric Field
A wooden block of mass M lies on a rough floor. Another wooden block of the same mass is hanging from the point O through strings as shown in the figure. To achieve equilibrium, the coefficient of static friction between the block on the floor and the floor itself is
- KCET - 2025
- Newtons Laws of Motion
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.