How many different ways can the letter of the word fudge arranged such that the vowels always come together?
Question Detail
Answer: Option A Show
Explanation: word SIGNATURE contains total 9 letters. Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now Required number of ways = 720*24 = 17280 Similar Questions : 1. Evaluate permutation equation \begin{aligned} ^{59}{P}_3 \end{aligned}
Answer: Option C Explanation: \begin{aligned} 2. In how many words can be formed by using all letters of the word BHOPAL
Answer: Option D Explanation: Required number 3. How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.
Answer: Option A Explanation: word SIGNATURE contains total 9 letters. Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now Required number of ways = 720*24 = 17280 4. 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] \\ 5. In how many ways can the letters of the word "CORPORATION" be arranged so that vowels always come together.
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 Read more from - Permutation and Combination Questions Answers In how many different ways can the letters of the word TRAINER be arranged so that the vowels always come together?A. 1440B. 120C. 720D. 360Answer Verified
Hint: To solve this problem we have to know about the concept of permutations and combinations. But here a simple concept is used. In any given word, the number of ways we can arrange the word by jumbling the letters is the number of letters present in the word factorial. Here factorial of any number is the product of that number and all the numbers less than that number till 1. Complete step by step answer: The number of ways the word TRAINER can be arranged so that the vowels always come together are 360. Note: Here while solving such kind of problems if there is any word of $n$ letters and a letter is repeating for $r$ times in it, then it can be arranged in $\dfrac{{n!}}{{r!}}$ number of ways. If there are many letters repeating for a distinct number of times, such as a word of $n$ letters and ${r_1}$ repeated items, ${r_2}$ repeated items,…….${r_k}$ repeated items, then it is arranged in $\dfrac{{n!}}{{{r_1}!{r_2}!......{r_k}!}}$ number of ways. How many different ways can the letters of the word fudge be arranged such that the vowels always come together?Required number of ways = (120 x 6) = 720.
How many ways word arrange can be arranged in which vowels are together?The number of ways the word TRAINER can be arranged so that the vowels always come together are 360.
How many ways leading can be arranged so that vowels come together?The word 'LEADING' has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter. Then, we have to arrange the letters LNDG (EAI). Now, 5 (4 + 1 = 5) letters can be arranged in 5!
...
Permutation-and-Combination.. How many different ways can letters of the word judge can be arranged?= 48. Q. In how many different ways can the letters of the word CHASE be arranged such that the vowels always come together.
|