AP EAMCET · Maths · Permutation Combination
The English alphabets have 5 vowels and 21 consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?
- A \(2100 \times 2 !\)
- B \(210 \times 2 !\)
- C \(210 \times 4 !\)
- D \(2100 \times 4 !\)
Answer & Solution
Correct Answer
(D) \(2100 \times 4 !\)
Step-by-step Solution
Detailed explanation
Selection of two vowels \(\Rightarrow{ }^5 \mathrm{C}_2\) Selection of two consonants \(\Rightarrow{ }^{21} C_2\) Arrangements of four letters \(\Rightarrow 4\) ! \(\therefore\) Total words \(={ }^5 C_2 \times{ }^{21} C_2 \times 4 !=2100 \times 4 !\)
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