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- Subject
- Permutations and Combinationsmathematics-mcqs › permutations-and-combinations
- Published
- 24 Jul 2019
- Last updated
- 28 May 2026
Explanation
The word 'OPTICAL' has 7 letters with vowels O, I, A. Treating the vowels as a single unit, we have 5 units to arrange (the vowel block plus the 4 consonants). The number of ways to arrange these units is 5! = 120. The vowels within the block can be arranged among themselves in 3! = 6 ways. Therefore, the total number of arrangements is 5! × 3! = 120 × 6 = 720.
More Permutations and Combinations MCQs
Practice related questions from the same subject.
- 1.Three flags, each of a distinct color, are used in a military drill to create different signaling codes by waving: I. A single flag of any color II. Any two flags in a specific order III. All three flags in various sequences What is the maximum number of unique codes that can be formed?
- 2.A question paper contains five problems, each with three internal options. In how many different ways can a candidate attempt at least one problem by choosing one option per problem?
- 3.There are 20 male students and 25 female students in a class. How many different pairs consisting of one boy and one girl can be formed?
- 4.How many different ways can you choose three consonants and two vowels from the letters in the word "TRIANGLE"?
- 5.A container holds 9 yellow balls, 3 white balls, and 4 red balls. How many different ways can you select two balls from this collection?
- 6.Using the digits {1, 2, 3, 5, 7, 9}, how many distinct four-digit even numbers can be created?
- 7.Using the digits {1, 3, 4, 5, 7, 9} without repeating any digit, how many unique four-digit numbers can be created?
- 8.In how many different ways can six boys and six girls be arranged in a single row for a photograph such that no two girls are seated next to each other?
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