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  • Question
  • From 5 consonants and 4 vowels, how many words can be formed using 3 consonants and 2 vowels ?


  • Options
  • A. 7600
  • B. 7200
  • C. 6400
  • D. 3600

  • Correct Answer
  • 7200 

    Explanation

    From 5 consonants, 3 consonants can be selected in  5 C 3  ways.

     

    From 4 vowels, 2 vowels can be selected in  4 C 2  ways.

     

    Now with every selection, number of ways of arranging 5 letters is 5 P 5 ways.

     

    Total number of words =  5 C 3 * 4 C 2 * 5 P 5

     

                                    = 10x 6 x 5 x 4 x 3 x 2 x 1= 7200


  • Permutation and Combination problems


    Search Results


    • 1. How many arrangements of the letters of the word ?BENGALI? can be made if the vowels are to occupy only odd places.

    • Options
    • A. 720
    • B. 576
    • C. 567
    • D. 625
    • Discuss
    • 2. Find the number of subsets of the set {1,2,3,4,5,6,7,8,9,10,11} having 4 elements.

    • Options
    • A. 340
    • B. 370
    • C. 320
    • D. 330
    • Discuss
    • 3. In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels always come together?

    • Options
    • A. 720
    • B. 1440
    • C. 1800
    • D. 3600
    • Discuss
    • 4. The number of ways in which 8 distinct toys can be distributed among 5 children?

    • Options
    • A. 5P8
    • B. 5^8
    • C. 8P5
    • D. 8^5
    • Discuss
    • 5. How many 6-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that the digits should not repeat and the second last digit is even ?

    • Options
    • A. 521
    • B. 720
    • C. 420
    • D. 225
    • Discuss
    • 6. There are three rooms in a Hotel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?

    • Options
    • A. 105
    • B. 7! x 6!
    • C. 7!/5!
    • D. 420
    • Discuss
    • 7. In how many ways the letters of the word OLIVER be arranged so that the vowels in the word always occur in the dictionary order as we move from left to right ?

    • Options
    • A. 186
    • B. 144
    • C. 136
    • D. 120
    • Discuss
    • 8. Nine different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, how many such words can be formed which have at least one letter repeated ?

    • Options
    • A. 43929
    • B. 59049
    • C. 15120
    • D. 0
    • Discuss
    • 9. To fill 8 vacancies there are 15 candidates of which 5 are from ST. If 3 of the vacancies are reserved for ST candidates while the rest are open to all, Find the number of ways in which the selection can be done ?

    • Options
    • A. 7920
    • B. 74841
    • C. 14874
    • D. 10213
    • Discuss
    • 10. The number of ways that 7 teachers and 6 students can sit around a table so that no two students are together is

    • Options
    • A. 7! x 7!
    • B. 7! x 6!
    • C. 6! x 6!
    • D. 7! x 5!
    • Discuss


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