in how many ways can the letters of the word , ' KEYBOARD ' be arranged in…
2024
in how many ways can the letters of the word , ' KEYBOARD ' be arranged in such a way that the vowels always come together ?
- A.
4250
- B.
4520
- C.
4320
- D.
4230
Attempted by 20 students.
Show answer & explanation
Correct answer: C
Answer: 4320
Key idea: Treat the vowels E, O, A as a single block so they always come together.
Count the items when vowels are a block: 5 consonants (K, Y, B, R, D) + 1 vowel-block = 6 items, which can be arranged in 6! = 720 ways.
Arrange the vowels inside the block: 3! = 6 ways.
Multiply the two results: 720 × 6 = 4320.
Note: All letters in KEYBOARD are distinct, so no further division is necessary.