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  • Question
  • 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

  • Correct Answer
  • 24 

    Explanation

    If a card hand that consists of four Queens and an Ace is rearranged, nothing has changed.

     

    The hand still contains four Queens and an Ace. Thus, use the combination formula for problems with cards.

     

    We have 4 eights and 4 sevens.

    We want 3 eights and 2 sevens.

    C(have 4 eights, want 3 eights) x C(have 4 sevens, want 2 sevens) 

    C(4,3) x C(4,2) = 24

     

    Therefore there are 24 different ways in which to deal the desired hand.


  • Permutation and Combination problems


    Search Results


    • 1. 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
    • 2. 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
    • 3. 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
    • 4. 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
    • 5. 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
    • 6. 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
    • 7. 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
    • 8. 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
    • 9. From a deck of 52 cards, a 5 card hand is dealt.How many distinct hands can be formed if there are atleast 2 queens?

    • Options
    • A. 103336
    • B. 120000
    • C. 108336
    • D. 108333
    • Discuss
    • 10. A student council of 5 members is to be formed from a selection pool of 6 boys and 8 girls.How many councils can have Jason on the council?

    • Options
    • A. 715
    • B. 725
    • C. 419
    • D. 341
    • Discuss


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