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  • Question
  • 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

  • Correct Answer
  • 65000 

    Explanation

    Out of 26 alphabets two distinct letters can be chosen in  26 P 2  ways. Coming to numbers part, there are 10 ways.(any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10ways to choose the second digit. Hence there are totally 10X10 = 100 ways. 

     

    Combined with letters there are  6 P 2  X 100 ways = 65000 ways to choose vehicle numbers.


  • Permutation and Combination problems


    Search Results


    • 1. 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
    • 2. 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
    • 3. 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
    • 4. 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
    • 5. From a pack of 52 cards, 3 cards are drawn together atrandom, What is the probability of both the cards are king?

    • Options
    • A. 1/5225
    • B. 1/5525
    • C. 5525
    • D. 1/525
    • Discuss
    • 6. 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
    • Discuss
    • 7. 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
    • 8. 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
    • 9. 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
    • 10. 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


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