In how many ways can the letters of the word 'LEADER' be arranged?A. 72 Show
B. 144 C. 360 D. 720 E. None of these Answer: Option C Solution(By Examveda Team) The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R. Click here to read 1000+ Related Questions on Permutation and Combination(Arithmetic Ability)Answer Verified Hint: The word daughter has $8$ letters in which $3$ are vowels. For the vowels
to always come together consider all the $3$ vowels to be one letter (suppose V) then total letters become $6$ which can be arranged in $6!$ ways and the vowels themselves in $3!$ ways.Complete step-by-step answer: (ii)We have to find the number of words formed when no vowels are together. Note:
Combination is used when things are to be arranged but not necessarily in order. Permutation is a little different. In permutation, order is important. Permutation is given by- Example from the textbook: Question: Sorry people I know most of u are too smart for this question, but I really need help so for questions c, d, e and f I have solved already, but I don't think my method of solving them is correct. G is the one I struggled for hours. info I already know 8 letters, 3 vowels (A,E,I) and 5 consonants (C,T,R,N,G) My Working Out for c, i did 3 x 4 x 5 x 4 x 3 which equals to 720 which is correct. for d, i did (3 x 4) - (2 x 3) first which equals to 6 I then multiply it by 3, 2, 5, 4 together therefore the final answer is 720. See in the first part I multiply 3 (the number of vowels) by 4 the number of position as any of the three vowels can fit in any of the 4 spaces. The questions asks for two vowels, since 1 vowel is already in one space the second vowel has two of the 3 vowels to take from and any of the two vowels can fit into the 3 remaining spaces. I subtract, because my intuition tells me to do so. for e, I did (3 x 4) - (2 x 3) - (1 x 2) first which equals to 4 I then multiply it by 3, 2, 1, 5 together, making the answer is 120 which is the right answer. Here, I follow the my own principle from d. So I'm not sure if I'm right. for f, I got the total arrangements from question a minus the total amount of words without vowels. To get the words without vowels i found all four letter arrangement words with consonants only which is 120. 1680 (from a) - 120 = 1560 (Correct) for g, I totally don't understand it, but the answer is 18 000. How many ways the letter Leading can be arranged so that vowels come together?= 120 ways. The vowels (EAI) can be arranged among themselves in 3! = 6 ways. Required number of ways = (120 x 6) = 720.
How many ways word leader can be arranged?∴ The total number of ways is 360.
How many ways vowels 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 letter leading? Required number of ways = (120 x 6) = 720. The word 'LEADING' has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter.
|