How many words can be formed from the letters of vowels always come at the odd places?
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Given as Show
The word ‘ORIENTAL’ The number of vowels in the word ‘ORIENTAL’ = 4(O, I, E, A) The number of consonants in given word = 4(R, N, T, L) The odd positions are (1, 3, 5 or 7) The four vowels can be arranged in these 4 odd places in 4P4 ways. And the remaining 4 even places (2,4,6,8) are to be occupied by the 4 consonants in 4P4 ways. Therefore, by using the formula, P (n, r) = n!/(n – r)! P (4, 4) × P (4, 4) = 4!/(4 – 4)! × 4!/(4 – 4)! = 4! × 4! = 4 × 3 × 2 × 1 × 4 × 3 × 2 × 1 = 24 × 24 = 576 Thus, the number of arrangements therefore that the vowels occupy only odd positions is 576. Nội dung chính Show
How many words can be formed by using the letters of the word ‘ORIENTAL’ so that A and E always occupy the odd places? Number of letters in word 'ORIENTAL' = 8 (all distinct) Number of letters to be used = 8 Step I: A and E are to occupy odd places marked X Number of letters = 2 (A and E) Number of boxes = 4 n = 4, r = 2Number of permutations of arranging A and E = ...(i) Step II: After A and E are fixed, there will be 6 letters left and 6 boxes for them. (A and E use up two boxes) Number of permutations of arrranging the remaining letters = ...(ii)Hence, from (i) and (ii), the total number of words formed = 12 x 720 = 8640. 427 Views A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there? Event 1: A coin is tossed and the outcomes recorded. Number of outcomes m = 2Event 2: The coin is tossed again and the outcomes recorded. Number of outcomes n = 2Event 3: The coin is tossed third time and the outcomes recorded. Number of outcomes p = 2∴ By fundamental principle of counting, the total number of outcomes recorded = 548 Views How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed. Number of digits available = 5 Number of places for the digits = 3. Number of ways in which place (x) can be filled = 5 m = 5 Number of ways in which place (y) can be filled = 5 (∵ Repetition is allowed) n = 5 Number of ways in which place (z) can be filled = 5 (∵ Repetition is allowed) p = 5 ∴ By fundamental principle of counting, the number of 3-digit numbers formed. = m x n x p = 5 x 5 x 5 = 125 458 Views How many 5-digit telephone numbers can be constructed, using the digits 0 to 9 if each number starts with 67 and no digit appears more than once ? Five of the 10-digits (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) are to be used. Number of ways of filling box (v) = 1
(∵ Only by 6) Number of ways of filling box (u) = 1
(∵ Only by 7) Number of ways of filling box (z) = 8
(∵ 6 and 7 are not allowed) Number of ways of filling box (y) = 7 (∵
Repetition is not allowed) Number of ways of filling box (x) = 6 (∵ Repetition is not
allowed) ∴ Total number of 5-digit telephone numbers formed = m x n x p x q x r = 1 x 1 x 8 x 7 x 6 = 336 138 Views How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed. Number of ways in which place (x) can be filled = 5 m = 5 Number of ways in which place (y) can be filled = 4 (∵ Repetition is not allowed) n = 4 Number of ways in which place (z) can be filled = 3 (∵ Repetition is not allowed) p = 3 ∴ By fundamental principle of counting, the total number of 3 digit numbers formed = m x n x p = 5 x 4 x 3 = 60. 526 Views Given 5 flags of different colours, how many different signals can be generated if each signal requires use of 2 flags, one below the other? Number of ways of finding a flag for place 1 = 5 m = 5Number of remaining flags = 4 Number of ways of finding a flag for place 2 to complete the signal = 4 n = 4∴ By fundamental principle of counting, the number of signals generated = 991 Views How many words can be formed with the letters of the word ORDINATE vowels occupy odd places?` How many words can be formed by article so that vowels occupy even places?We can form 144 words with the letters of the word ARTICLE where vowels occupy the even places and consonants the odd places. How many ways can the letters of the word strange be arranged so that the vowels come together?(a) There are 7 letters in the word 'STRANGE' amongst which 2 are vowels and there are 4 odd places (1, 3, 5, 7) where these two vowels are to be placed together. And corresponding to these 12 ways the other 5 letters may be placed in 5! ways =5×4×3×2×1=120. How many words can be formed with Oriental so that A and E occupy odd places?Permutations and Combinations How many words can be formed by using the letters of the word 'ORIENTAL' so that A and E always occupy the odd places? Step II: After A and E are fixed, there will be 6 letters left and 6 boxes for them. Hence, from (i) and (ii), the total number of words formed = 12 x 720 = 8640. How many words can be formed from letters of word article if vowels come at odd places?Total no. of words formed=4×24×6=576.
How many words can be formed the vowels may occupy only odd places?Hence, the number of words where vowels occupy odd places are 576.
How many words can be formed from the letters of the word vowels?1 Answer. The word VOWELS contain 6 letters. The permutation of letters of the word will be 6! = 720 words.
How many words can be formed so that the vowels occupy the even places?We can form 144 words with the letters of the word ARTICLE where vowels occupy the even places and consonants the odd places.
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