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Answer : D Solution : CORPORATION is 11 letter word. <br> It has 5 vowels (O, O, O, A, I) and 6 consonants (C, R, P, R, T, N) <br> In 11 letters, there are 5 even places `(2^(nd), 4^(th), 6^(th), 8^(th) and 10^(th) " positions")` <br> 5 vowels can take 5 even places in `(5!)/(3!)` ways ( `:'` Since O is repeated thrice) <br> Similarly, 6 consonasts can take 6 odd places in `(6!)/(2!)` ways <br> ( `:'` R is repeated twice) <br> `:.` Total number of ways `= (5!)/(3!) xx (6!)/(2!) = 20 xx 360 = 7200` In how many different ways can the letters of the word 'CORPORATION' be arranged, so that the vowels always come together? Options
Solution50400 In the word 'CORPORATION', we treat the vowels OOAlO as one letter. = `(7!)/(2!)=2520` Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in `(5!)/(3!)=20` ways ∴ Required number of ways Concept: Permutation and Combination (Entrance Exam) Is there an error in this question or solution? Correct Answer - Option 4 : 50400 Concept:
Calculation: The word CORPORATION has 11 letters out of which 6 are consonants (CRPRTN) and 5 are vowels (OOAIO). Considering the objects of the same type, the number of arrangements of these vowels will be \(\rm \dfrac{5!}{3!}\) = 20. Since, the vowels have to be together, we can say that we have to arrange the groups (C), (R), (P), (R), (T), (N) and (OOAIO) among themselves. Considering the objects of the same type, this can be done in \(\rm \dfrac{7!}{2!}\) = 2520 ways. And, total number of arrangements of all the letters = [Number of arrangements of (C), (R), (P), (R), (T), (N) and (OOAIO)] × [Number of arrangements of (OOAIO)] = 20 × 2520 = 50400. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?A. 810 B. 1440 C. 2880 D. 50400 E. 5760 Answer: Option D Solution(By Examveda Team) In the word 'CORPORATION', we treat the vowels OOAIO as one letter. Click here to read 1000+ Related Questions on Permutation and Combination(Arithmetic Ability)Question Detail
Answer: Option B Explanation: Vowels in the word "CORPORATION" are O,O,A,I,O This has 7 lettes, where R is twice so value = 7!/2! Vowel O is 3 times, so vowels can be arranged = 5!/3! = 20 Total number of words = 2520 * 20 = 50400 Similar Questions : 1. In how many ways can the letters of the CHEATER be arranged
Answer: Option B Explanation: As we can see the letter "E" is twice in given word, so Required Number 2. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done
Answer: Option D Explanation: From a group of 7 men and 6 women, five persons are to be selected with at least 3 men. \begin{aligned}
= \left[\dfrac{7 \times 6 }{2 \times 1}\right] + \left[\left( \dfrac{7 \times 6 \times 5}{3 \times 2 \times 1} \right) \times 6 \right] + \\ \left[\left( \dfrac{7 \times 6 \times 5}{3 \times 2 \times 1} \right) \times \left( \dfrac{6 \times 5}{2 \times 1} \right) \right] \\ 3. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there
Answer: Option D Explanation: In a group of 6 boys and 4 girls, four children are to be selected such that (four boys) or (three boys and one girl) or (two boys and two girls) or (one boy and three gils) This combination question can be solved as \begin{aligned} = \left[\dfrac{6 \times 5 }{2 \times 1}\right] + \left[\left(\dfrac{6 \times 5 \times 4 }{3 \times 2 \times 1}\right) \times 4\right] + \\\left[\left(\dfrac{6 \times 5 }{2 \times 1}\right)\left(\dfrac{4 \times 3 }{2 \times 1}\right)\right] + \left[6 \times 4 \right] \\ 4. A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw
Answer: Option A Explanation: From 2 white balls, 3 black balls and 4 red balls, 3 balls are to be selected such that Hence we have 3 choices \begin{aligned} 5. In how many way the letter of the word "RUMOUR" can be arranged
Answer: Option D Explanation: In above word, there are 2 "R" and 2 "U" \begin{aligned} Read more from - Permutation and Combination Questions Answers How many different types of arrangement are possible so that the vowels are always together?The number of ways the word TRAINER can be arranged so that the vowels always come together are 360.
How many different ways can the word corporation be arranged?Therefore, Required number of ways =(2520×20)=50400.
How many ways the word vowel can be arranged so that the vowels come together?So by adding up three we get 48+48+48=144 is the required solution.
How many ways can the letters be arranged so that all the vowels come together word is impossible?In how many ways can the letters of the word IMPOSSIBLE be arranged so that all the vowels come together? Now count the ways the vowels in the super letter can be arranged, since there are 4 and 1 2-letter(I'i) repeat the super letter of vowels would be arranged in 12 ways i.e., (4!/2!) = (7!/2! × 4!/2!)
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