Discussion
In how many different ways can the letters of the word ‘GEOMETRY’ be arranged so that the vowels always come together?
Answer: C
GEOMETRY has eight letters with E appearing twice. Its vowels are E, O, E.
Treat the three vowels as one block, giving six units to arrange (the block plus G, M, T, R, Y):
\[ 6! = 720 \]
Within the block the three vowels can be ordered in
\[ \frac{3!}{2!} = 3 \text{ ways} \]
since the two E's are identical.
\[ 720 \times 3 = 2160 \]
Treating the E's as distinguishable would give \( 720 \times 6 = 4320 \) - double-counting every arrangement, because swapping the two E's changes nothing visible.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development