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Home Aptitude Permutation and Combination Comments

  • Question
  • 12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?


  • Options
  • A. 500
  • B. 490
  • C. 495
  • D. 540

  • Correct Answer
  • 495 

    Explanation

    For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is  12 C 4  = 495.

     

    Therefore, we can draw 495 quadrilaterals


  • Permutation and Combination problems


    Search Results


    • 1. Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct

    • Options
    • A. 65000
    • B. 64000
    • C. 72000
    • D. 36000
    • Discuss
    • 2. In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

    • Options
    • A. 120960
    • B. 120000
    • C. 146700
    • D. None of these
    • Discuss
    • 3. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

    • Options
    • A. 11670
    • B. 12000
    • C. 11760
    • D. 20050
    • Discuss
    • 4. Suppose you can travel from a place A to a place B by 3 buses, from place B to place C by 4 buses, from place C to place D by 2 buses and from place D to place E by 3 buses. In how many ways can you travel ?from A to E?

    • Options
    • A. 36
    • B. 64
    • C. 74
    • D. 72
    • Discuss
    • 5. In a G - 20 meeting there were total 20 people representing their own country. All the representative sat around a circular table. Find the number of ways in which we can arrange them around a circular table so that there is exactly one person between two representatives namely Manmohan and Musharraf.

    • Options
    • A. 2 x (17!)
    • B. 2 x (18!)
    • C. (3!) x (18!)
    • D. (17!)
    • Discuss
    • 6. Find the number of ways to take 4 people and place them in groups of 3 at a time where order does not matter?

    • Options
    • A. 4
    • B. 12
    • C. 36
    • D. 16
    • Discuss
    • 7. How many ways are there to deal a five-card hand consisting of three eight's and two sevens?

    • Options
    • A. 36
    • B. 72
    • C. 24
    • D. 16
    • Discuss
    • 8. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

    • Options
    • A. 4!/2!
    • B. 3!/2!
    • C. (4! x 3!) / 2!
    • D. 36
    • Discuss
    • 9. In how many ways can the letters of the word "PROBLEM" be rearranged to make 7 letter words such that none of the letters repeat?

    • Options
    • A. 49
    • B. 7!
    • C. 7^7
    • D. 7^3
    • Discuss
    • 10. There are fourteen juniors and twenty-three seniors in the Service Club. The club is to send four representatives to the State Conference. If the members of the club decide to send two juniors and two seniors, how many different groupings are possible ?

    • Options
    • A. 23024
    • B. 24023
    • C. 23023
    • D. 25690
    • Discuss


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