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Permutation and Combination

  1. If 56Pr + 6 : 54Pr + 3 = 30800 : 1 then the value of r is ?
    1. 40
    2. 41
    3. 42
    4. None of these
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    56Pr + 6 : 54Pr + 3 = 30800 : 1
    ⇒ 56! / (50 - r)! = (30800 x 54!) / (51-r!)

    Correct Option: B

    56Pr + 6 : 54Pr + 3 = 30800 : 1
    ⇒ 56! / (50 - r)! = (30800 x 54!) / (51-r!)
    ⇒ 56 x 55 = 30800/(51 - r)
    ⇒ 51 - r = 10
    ∴ r = 41

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  1. How many groups of 6 persons can be formed from 8 men and 7 women ?
    1. 5000
    2. 5005
    3. 5050
    4. None of these
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    Total no . of person = 8 + 7 = 15
    No. of groups = 15C6

    Correct Option: B

    Total no . of person = 8 + 7 = 15
    No. of groups = 15C6 = 15! / {6! (15 - 6)!} = 15! / (6! 9!)
    = (15 x 14 x 13 x 12 x 11 x 10) / (6 x 5 x 4 x 3 x 2 x 1)
    = 5005

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  1. There are 10 oranges in a basket. Find the no. of ways in which 3 oranges are chosen from the basket ?
    1. 125
    2. 140
    3. 110
    4. 120
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    Required number of ways = 10C3

    Correct Option: D

    Required number of ways = 10C3
    = 10!/ {3! (10 - 3)!} = 10! / (3! 7!) = (10 x 9 x 8) / (3 x 2) = 120

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  1. There are 25 students in a class. Find the number of ways in which a committee of 3 students is to be formed. ?
    1. 2200
    2. 2300
    3. 2400
    4. 3200
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    Required number of ways = 25C3

    Correct Option: B

    Required number of ways = 25C3
    = (25 x 24 x 23) / (1 x 2 x 3) = 2300

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  1. 8 men entered a lounge simultaneously. If each person shook hands with the other, then find the total no. of hand shakes ?
    1. 16
    2. 36
    3. 56
    4. 28
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    Required no. of hand shakes = {8 x (8 - 1)}/2 = 28

    Correct Option: D

    Required no. of hand shakes = {8 x (8 - 1)}/2 = 28

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