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  • Question
  • In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?


  • Options
  • A. 36
  • B. 25
  • C. 42
  • D. 120

  • Correct Answer
  • 36 

    Explanation

    There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.

     

    Let us mark these positions as under: 

                                                          (1) (2) (3) (4) (5) (6) 

    Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.  

    Number of ways of arranging the vowels = 3 P 3  = 3! = 6.

     

    Also, the 3 consonants can be arranged at the remaining 3 positions. 

    Number of ways of these arrangements =  3 P 3  = 3! = 6. 

    Total number of ways = (6 x 6) = 36.


  • Permutation and Combination problems


    Search Results


    • 1. In how many ways the letters of the word 'DESIGN' can be arranged so that no consonant appears at either of the two ends?

    • Options
    • A. 240
    • B. 72
    • C. 48
    • D. 36
    • Discuss
    • 2. A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?

    • Options
    • A. 123
    • B. 113
    • C. 246
    • D. 945
    • Discuss
    • 3. In how many different ways can the letters of the word 'RITUAL' be arranged?

    • Options
    • A. 720
    • B. 5040
    • C. 360
    • D. 180
    • Discuss
    • 4. A card is drawn from a pack of 52 cards. What is the probability that either card is black or a king?

    • Options
    • A. 15/52
    • B. 17/26
    • C. 13/17
    • D. 15/26
    • Discuss
    • 5. From a bunch of flowers having 16 red roses and 14 white roses, four flowers have to be selected. In how many different ways can they be selected such that at least one red rose is selected?

    • Options
    • A. 27405
    • B. 26584
    • C. 26585
    • D. 27404
    • Discuss
    • 6. Consider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter palindromes.

    • Options
    • A. 17756
    • B. 17576
    • C. 12657
    • D. 12666
    • Discuss
    • 7. How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters ?

    • Options
    • A. 5^10
    • B. 10^5
    • C. 5P5
    • D. 5C5
    • Discuss
    • 8. How many words can be formed with or without meaning by using three letters out of k, l, m, n, o without repetition of alphabets.

    • Options
    • A. 60
    • B. 120
    • C. 240
    • D. 30
    • Discuss
    • 9. If (1 × 2 × 3 × 4 ........ × n) = n!, then 15! - 14! - 13! is equal to ___?

    • Options
    • A. 14 × 13 × 13!
    • B. 15 × 14 × 14!
    • C. 14 × 12 × 12!
    • D. 15 × 13 × 13!
    • Discuss
    • 10. A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow ?

    • Options
    • A. 3/17
    • B. 4/21
    • C. 2/21
    • D. 5/17
    • Discuss


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