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
- 5780
- 2890
- 5440
- 2720
The Correct Option is A
Solution and Explanation
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 $=(17)^{2} \cdot 20=5780$.
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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