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Previous Year Question (PYQs)



Out of 5 consonants and 4 vowels, how many words of 3 consonants and 3 vowels can be made? 
1.40 
2.80 
3.20 
4.240





Solution

We have 5 consonants and 4 vowels. We need to form a word with 3 consonants and 3 vowels.

Step 1: Choose consonants

\[ \binom{5}{3} = 10 \]

Step 2: Choose vowels

\[ \binom{4}{3} = 4 \]

Step 3: Arrange the chosen 6 letters

\[ 6! = 720 \]

Step 4: Total words

\[ 10 \times 4 \times 720 = 28800 \]

Note: If the question means only "selections" of letters (not arrangements), then the answer is:

\[ \binom{5}{3}\times \binom{4}{3} = 10 \times 4 = 40 \]

Final Answer:

- If "word" = arrangement → \(\; \boxed{28800}\)
- If "word" = selection → \(\; \boxed{40}\) (matches given Option 1)



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