Question

How many words each of two vowels and three consonants can be formed from the letters of the word "UNIVERSAL"?

• A. 7000
• B. 7200
• C. 7400
• D. 7800

Hint:

Choose 2 vowels and 3 consonants separately, then arrange all 5 letters.

Answer 1

The Correct Option is B

Step 1: Build the word position by position instead of selecting letters first.
$U, N, I, V, E, R, S, A, L$ splits into 4 vowels ($U, I, E, A$) and 5 consonants ($N, V, R, S, L$), same as before, but now we place letters straight into positions.

Step 2: Pick and order 2 vowels from the 4 available.
Picking 2 vowels and fixing their order at the same time is a permutation: $^4P_2 = 4 \times 3 = 12$ ways.

Step 3: Pick and order 3 consonants from the 5 available.
$^5P_3 = 5 \times 4 \times 3 = 60$ ways.

Step 4: Decide which of the 5 word positions belong to vowels.
Out of 5 slots in the word, we choose 2 for the vowels and the rest go to consonants: $^5C_2 = 10$ ways.

Step 5: Multiply everything together.
Total words $= 12 \times 60 \times 10 = 7200$.

Final Answer:
Building the word position by position instead of selecting the letters first, we again get 7200 words.
\[ \boxed{7200} \]