Question:
With $17$ consonants and $5$ vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is
With $17$ consonants and $5$ vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is
Updated On: Jan 30, 2025
- 5780
- 2890
- 5440
- 2720
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The two letters, the first and the last of the four lettered word can be chosen in $(17)^{2}$ ways, as repetition is allowed for consonants.
The two vowels in the middle are distinct so that the number of ways of filling up the two places is ${ }^{5} P_{2}=20$.
The no. of different words $=(17)^{2} \cdot 20=5780$.
The two vowels in the middle are distinct so that the number of ways of filling up the two places is ${ }^{5} P_{2}=20$.
The no. of different words $=(17)^{2} \cdot 20=5780$.
Was this answer helpful?
1
0
Top Questions on sequences
- 10, 30, 68, 130, ___ ,350
find the missing number? - Let $a_1=8, a_2, a_3, \ldots, a_n$ be an AP If the sum of its first four terms is $50$ and the sum of its last four terms is $170$ , then the product of its middle two terms is______
- Using mathematical induction, the numbers $ a_n $ are defined by $ a_0 = 1, a_{n+1} = 3n^2 + n + a_n, (n \geq 0) $. Then, $ a_n $ is equal to
If aa is the greatest term in the sequence \(a_n=\frac{n^3}{n^4+147},n=1,2,3,...,\) then a is equal to______________.
- The statement $(p \wedge(\sim q)) \Rightarrow(p \Rightarrow(\sim q))$ is
View More Questions
Questions Asked in BITSAT exam
- What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
- BITSAT - 2025
- Vector Algebra
- The sum of the first 30 terms of an arithmetic progression is 930. If the first term is 2, what is the common difference of the progression?
- BITSAT - 2025
- Arithmetic Progression
If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are real and equal, then:
- BITSAT - 2025
- Quadratic Equations
- If log$_{10}$(x + 1) = 2, what is the value of x?
- BITSAT - 2025
- Fundamental Theorem of Calculus
- Which number comes next in the series? 3, 6, 11, 18, 27, ?
- BITSAT - 2025
- Number Series
View More Questions
Concepts Used:
Sequences
A set of numbers that have been arranged or sorted in a definite order is called a sequence. The terms in a series mention the numbers in the sequence, and each term is distinguished or prominent from the others by a common difference. The end of the sequence is frequently represented by three linked dots, which specifies that the sequence is not broken and that it will continue further.
Read More: Sequence and Series
Types of Sequence:
There are four types of sequences such as:
- Arithmetic Sequence
- Fibonacci Sequence
- Geometric Sequence
- Harmonic Sequence