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  • Question
  • In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together


  • Options
  • A. 50000
  • B. 40500
  • C. 5040
  • D. 50400

  • Correct Answer
  • 50400 

    Explanation

    In the word 'CORPORATION', we treat the vowels OOAIO as one letter.

     

    Thus, we have CRPRTN (OOAIO).

     

    This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.

     

    Number of ways arranging these letters =7!/2!= 2520.

     

    Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in 3!/5!= 20 ways.

     

    Required number of ways = (2520 x 20) = 50400.


  • Permutation and Combination problems


    Search Results


    • 1. A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?

    • Options
    • A. 1260
    • B. 210
    • C. 210 x 6!
    • D. 1512
    • Discuss
    • 2. In the below word how many words are there in which R and W are at the end positions? RAINBOW

    • Options
    • A. 120
    • B. 180
    • C. 210
    • D. 240
    • Discuss
    • 3. If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word RECREATIONAL, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ?X? as the answer. If no such word can be formed, give ?Z? as the answer.

    • Options
    • A. T
    • B. X
    • C. N
    • D. R
    • Discuss
    • 4. How many four digit even numbers can be formed using the digits {2, 7, 5, 3, 9, 1} ?

    • Options
    • A. 59
    • B. 60
    • C. 61
    • D. 64
    • Discuss
    • 5. There are 41 students in a class, number of girls is one more than number of guys. we need to form a team of four students. all four in the team cannot be from same gender. number of girls and guys in the team should NOT be equal. How many ways can such a team be made ?

    • Options
    • A. 49450
    • B. 50540
    • C. 46587
    • D. 52487
    • Discuss
    • 6. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

    • Options
    • A. 54
    • B. 64
    • C. 63
    • D. 36
    • Discuss
    • 7. How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated ?

    • Options
    • A. 60
    • B. 26
    • C. 50
    • D. 64
    • Discuss
    • 8. Find the number of ways to arrange 4 people in groups of 3 at a time where order matters?

    • Options
    • A. 20
    • B. 16
    • C. 24
    • D. 36
    • Discuss
    • 9. Find the number of ways to arrange 6 items in groups of 4 at a time where order matters?

    • Options
    • A. 720
    • B. 640
    • C. 740
    • D. 360
    • Discuss
    • 10. Find the number of ways to take 20 objects and arrange them in groups of 5 at a time where order does not matter.?

    • Options
    • A. 57090
    • B. 15540
    • C. 15504
    • D. 23670
    • Discuss


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