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Home Aptitude Permutation and Combination Comments

  • Question
  • Goldenrod and No Hope are in a horse race with 6 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?


  • Options
  • A. 720
  • B. 360
  • C. 120
  • D. 640

  • Correct Answer
  • 360 

    Explanation

    Two horses A and B, in a race of 6 horses... A has to finish before B

     

    if A finishes 1... B could be in any of other 5 positions in 5 ways and other horses finish in 4! Ways, so total ways 5*4!

     

    if A finishes 2... B could be in any of the last 4 positions in 4 ways. But the other positions could be filled in 4! ways, so the total ways 4*4!

     

    if A finishes 3rd... B could be in any of last 3 positions in 3 ways, but the other positions could be filled in 4! ways, so total ways 3*4!

     

    if A finishes 4th... B could be in any of last 2 positions in 2 ways, but the other positions could be filled in 4! ways, so total ways... 2 * 4! 

     

    if A finishes 5th .. B has to be 6th and the top 4 positions could be filled in 4! ways..

     

    A cannot finish 6th, since he has to be ahead of B

     

    Therefore total number of ways = 5*4! + 4*4! + 3*4! + 2*4! + 4! = 120 + 96 + 72 + 48 + 24 = 360


  • Permutation and Combination problems


    Search Results


    • 1. In how many ways, can zero or more letters be selected form the letters AAAAA?

    • Options
    • A. 5
    • B. 6
    • C. 2
    • D. 8
    • Discuss
    • 2. In how many ways can the letters of the word 'MISSISIPPI' be arranged ?

    • Options
    • A. 12400
    • B. 11160
    • C. 16200
    • D. 12600
    • Discuss
    • 3. There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?

    • Options
    • A. 18! x 19!
    • B. 2 x 19!
    • C. 2 x 18!
    • D. 18! x 18!
    • Discuss
    • 4. Eight first class and six second class petty officers are on the board of the 56 club. In how many ways can the members elect, from the board, a president, a vice-president, a secretary, and a treasurer if the president and secretary must be first class petty officers and the vice-president and treasurer must be second class petty officers?

    • Options
    • A. 1500
    • B. 1860
    • C. 1680
    • D. 1640
    • Discuss
    • 5. A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

    • Options
    • A. 126
    • B. 240
    • C. 120
    • D. 260
    • Discuss
    • 6. A committee of 4 people is to be formed from a group of 9 people.How many possible committees can be formed?

    • Options
    • A. 120
    • B. 162
    • C. 126
    • D. 170
    • Discuss
    • 7. A pizza can have 3 toppings out of possible 7 toppings.How many different pizza's can be made?

    • Options
    • A. 49
    • B. 35
    • C. 27
    • D. 25
    • Discuss
    • 8. How many ways can you select 17 songs for mix CD out of possible 38 songs?

    • Options
    • A. 2878
    • B. 2878 x 10^2
    • C. 290183753
    • D. 2878 x 10^10
    • Discuss
    • 9. A school committee of 5 is to be formed from 12 students.How many committees can be formed if John must be on the committee?

    • Options
    • A. 11P4
    • B. 11C4
    • C. 11P5
    • D. 11C5
    • Discuss
    • 10. From a deck of 52 cards, a 7 card hand is dealt.How many distinct hands are there if the hand must contain 2 spades and 3 diamonds ?

    • Options
    • A. 7250100
    • B. 7690030
    • C. 7250000
    • D. 3454290
    • Discuss


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