CA Foundation · Quantitative Aptitude · Permutations and Combinations
In how many ways can the letters of the word 'LOGIC' be arranged such that the vowels are always together?
When vowels in LOGIC are kept together as a single unit, we get 4 units total. These arrange in 4! = 24 ways. The two vowels internally arrange in 2! = 2 ways. Total arrangements = 24 × 2 = 48.
- A12
- B24
- C48Correct
- D120
Explanation
LOGIC has 2 vowels (O, I) and 3 consonants (L, G, C). Treating the vowels as one unit, we have 4 units to arrange: (OI), L, G, C. These can be arranged in 4! = 24 ways. The vowels O and I can be arranged among themselves in 2! = 2 ways. Total = 24 × 2 = 48. Option 24 incorrectly omits the internal arrangement of vowels.
Did you get it right without looking?
One question tells you little. A timed set on Permutations and Combinations shows your real accuracy, how long you take and where you lose marks.
More Permutations and Combinations questions
- If nP2 = 90, what is the value of n?
- A surveyor marks 10 points on a plot map, of which exactly 4 lie on one straight line and no other three are collinear. How many triangles c…
- A password must contain exactly 8 characters: a mix of digits (0–9) and uppercase English letters (A–Z). The first character must be a lette…
- A shopkeeper in Jaipur distributes 10 identical laddus among 3 children so that each child gets at least one laddu. In how many ways can thi…
- How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6 where no digit is repeated?
- How many distinct arrangements of the letters of the word COMMITTEE are there in which all the vowels stay together?