Quantitative Aptitude: Permutations and Combinations Set 3

  1. Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
    575
    729
    615
    683
    None
    Option B
    Solution:
    The 1st ring can be worn in any of the 3 fingers.
    Similarly each of the remaining 5 rings also can be worn in 3 ways.
    No of ways=3*3*3*3*3*3=36=729.

     

  2. In a birthday party, every person shakes hand with every other person. If there was a total of 28 handshakes in the party, how many persons were present in the party?
    6
    12
    10
    8
    None
    Option D
    Solution:
    Let n be the total number of persons present in the party.
    No of handshake= [n(n-1)] /2 =28
    n(n-1) = 56
    n=8.

     

  3. In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate?
    70
    68
    72
    65
    None
    Option C
    Solution:
    There are 3boys and 3girls.
    Alternate arrangement BGBGBG or GBGBGB
    Then ways= (3!*3!) + (3!*3!)
    =36+36=72.

     

  4. In how many ways can 4 persons be chosen from 5 boys and 4 girls so as to include exactly one girl?
    40
    35
    50
    45
    None
    Option A
    Solution:
    Exactly 1 girl 4c1= 4.
    Remaining 3person selected from boys 5c3 =10.
    Total ways=4*10=40.

     

  5. A student is to answer 5 out of 10 questions in an examination such that he must choose at least 3 from the first five questions. The number of choices available to him is
    96
    115
    87
    126
    None
    Option D
    Solution:
    Ways 5c3*5c2 + 5c4*5c1 +5c5
    =100+25+1
    =126ways.

     

  6. In a bag there are five marbles of pink colour and six marbles of blue colour. Two marbles are chosen randomly. What is the probability that both are of same colour?
    6/14
    5/11
    5/14
    8/11
    None
    Option B
    Solution:
    Probability = 5c2/11c2 + 6c2/11c2
    = (5*4)/(11*10) + (6*5)/(11*10)
    = 2/11+ 3/11
    =5/11.

     

  7. A box contains 5 Green balls, 3 Red balls, 2 Blue balls and 2 Orange balls. If two balls are drawn at random, what is the probability that both are red?
    5/11
    3/22
    1/22
    2/11
    None
    Option C
    Solution:
    Total balls =5+3+2+2= 12
    Probability =3c2/12c2
    = (3*2) / (12*11)
    = 1/22.

     

  8. From a group of 5 men and 6 women, five persons are to be selected to form a committee so that at least 3 women are there on the committee. In how many ways can it be done?
    315
    266
    325
    281
    None
    Option D
    Solution:
    Possible ways= 3W and 2M or 4W and 1M or 5W
    (6c3*5c2) + (6c4*5c1) + 6c5
    [(6*5*4)/(3*2*1) * (5*4)/(2*1)] + [(6*5*4*3)/(4*3*2*1)*5] +6
    200+75+6
    =281ways.

     

  9. In how many different ways can the letters of the word ‘ APTITUDE ’ be arranged so that the vowels always come together?
    1440
    1950
    2125
    1645
    None
    Option A
    Solution:
    In a word APTITUDE there are 4vowels A, I, U, E.
    Ways= (5! *4! ) / 2!
    =1440.

     

  10. A boy has 3 library cards and 8 books of his interest are in the library. Of these 8, he does not want to borrow English part II unless English part I is also borrowed. In how many ways can he choose the three books to be borrowed?
    52
    41
    36
    46
    None
    Option B
    Solution:
    The first option is he chooses any of the books other then English part 2 = 7c3 = 35
    The second option is he selects both the English books and any other book from the remaining options = (2c2 * 6c1) = 6
    So total ways=41.

     



 

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