How many four digit numbers $abcd$ exist such that $a$ is odd, $b$ is divisible by $3$, $c$ is even and $d$ is prime?
- 380
- 360
- 400
- 520
The Correct Option is C
Solution and Explanation
$ \{1,3,5,7,9\} $
$\therefore n(a)=5$
Divisible by $3$ are $\{0,3,6,9\}, n(b)=4$
Even numbers are $\{0,2,4,6,8\}, n(c)=5$
and prime numbers are $\{2,3,5,7\}, n(d)=4$
$\therefore$ Four-digit numbers $abcd$ exist
$=5 \cdot 4 \cdot 5 \cdot 4$
$=400$
Top Questions on 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
- Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to:
- JEE Main - 2025
- Mathematics
- permutations and combinations
- The number of 6-letter words, with or without meaning, that can be formed using the letters of the word "MATHS" such that any letter that appears in the word must appear at least twice is:
- JEE Main - 2025
- Mathematics
- permutations and combinations
If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440th position in this arrangement is:
- JEE Main - 2025
- Mathematics
- permutations and combinations
- Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to:
- JEE Main - 2025
- Mathematics
- permutations and combinations
Questions Asked in KEAM exam
- If the lines \( \frac{x-1}{2} = \frac{y-2}{\alpha} = \frac{z-3}{2} \) and \( \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-3}{-2} \) are perpendicular, then the value of \( \alpha \) is:
- KEAM - 2024
- Integration
- In the measurement of length 6 $\mu$m is equal to $x$ pm. Then the value of $x$ is
- KEAM - 2024
- Dimensional Analysis
- An organic compound contains 37.5% C, 12.5% H and the rest oxygen. What is the empirical formula of the compound?
- KEAM - 2024
- Oxygen
- Let A, B, C denote the set of students in a college who play football, basketball, and cricket respectively. If \( n(A) = 60 \), \( n(B) = 55 \), \( n(C) = 70 \), \( n(A \cup B \cup C) = 100 \) and \( n(A \cap B \cap C) = 20 \), then the number of students who play exactly two of these sports is
- KEAM - 2024
- Relations and functions
For the reaction:
\[ 2A + B \rightarrow 2C + D \]
The following kinetic data were obtained for three different experiments performed at the same temperature:
\[ \begin{array}{|c|c|c|c|} \hline \text{Experiment} & [A]_0 \, (\text{M}) & [B]_0 \, (\text{M}) & \text{Initial rate} \, (\text{M/s}) \\ \hline I & 0.10 & 0.10 & 0.10 \\ II & 0.20 & 0.10 & 0.40 \\ III & 0.20 & 0.20 & 0.40 \\ \hline \end{array} \]
The total order and order in [B] for the reaction are respectively:
- KEAM - 2024
- Grignard’s reagents and their uses
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.