Basic Concepts Of Permutations And Combinations

20 Questions  I  By Sweetsalman123 on March 20, 2012
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»7«/mn»«mo»!«/mo»«/mrow»«mrow»«mn»3«/mn»«mo»!«/mo»«/mrow»«/mfrac»«/math»

  

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1.  If n1+n2 P2 = 132, n1-n2P2 = 30 then,  
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D.
2.  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»51«/mn»«mi»c«/mi»«/msub»«mn»31«/mn»«/msub»«/math» is equal to Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»51«/mn»«mi»c«/mi»«/msub»«mn»20«/mn»«/msub»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mo».«/mo»«msub»«msub»«mn»50«/mn»«mi»c«/mi»«/msub»«mn»20«/mn»«/msub»«/math» C.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mo».«/mo»«msub»«msub»«mn»45«/mn»«mi»c«/mi»«/msub»«mn»15«/mn»«/msub»«/math» D.None of these
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3.  If nc10 = nc14, then «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»25«/mn»«mi»c«/mi»«/msub»«mi»n«/mi»«/msub»«/math» is
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4.  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»n«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«msub»«mi»P«/mi»«mi»r«/mi»«/msub»«mo»§nbsp;«/mo»«mo»+«/mo»«mi»r«/mi»«mo».«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»n«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«msub»«mi»P«/mi»«mrow»«mo»(«/mo»«mi»r«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«/msub»«/math» is equal to Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mi»n«/mi»«mi»c«/mi»«/msub»«mi»r«/mi»«/msub»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»n«/mi»«mo»!«/mo»«/mrow»«mrow»«mo»(«/mo»«mi»r«/mi»«mo»!«/mo»«mo»(«/mo»«mi»n«/mi»«mo»-«/mo»«mi»r«/mi»«mo»)«/mo»«mo»!«/mo»«mo»)«/mo»«/mrow»«/mfrac»«/math» C.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mi»n«/mi»«mi»p«/mi»«/msub»«mi»r«/mi»«/msub»«/math» D.None of these
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5.  The number of ways in which 8 sweats of different sizes can be distributed among 8 persons of different ages so that the largest sweat always goes to be younger assuming that each one of then gets a sweat is
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D.
6.  The number of ways in which the letters of the word DOGMATIC can be arranged is
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7.  If 50 different jewels can be set to form a necklace then the number of ways is Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mn»50«/mn»«mo»!«/mo»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mn»49«/mn»«mo»!«/mo»«/math» C.49! D.None of these
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8.  The number of even numbers greater than 300 can be formed with the digits 1, 2, 3, 4, 5  without repetion is
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9.  A person has 8 friends. The number of ways in which he may invite one or more of thai to a dinner is.
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10.  The number of straight lines obtained by joining 16 points on a plane, no twice of them being on the same line is
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11.  The number of ways in which 7 girls form a ring is
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12.  The ways of selecting 4 letters from the word EXAMINATION is
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13.  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»n«/mi»«msub»«mi»C«/mi»«mn»1«/mn»«/msub»«/msub»«mo»+«/mo»«msub»«mi»n«/mi»«msub»«mi»c«/mi»«mn»2«/mn»«/msub»«/msub»«mo»+«/mo»«msub»«mi»n«/mi»«msub»«mi»c«/mi»«mn»3«/mn»«/msub»«/msub»«mo»+«/mo»«msub»«mi»n«/mi»«msub»«mi»c«/mi»«mn»4«/mn»«/msub»«/msub»«mo»+«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»+«/mo»«mi»e«/mi»«mi»q«/mi»«mi»u«/mi»«mi»a«/mi»«mi»l«/mi»«mi»s«/mi»«/math» Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»2«/mn»«mi»n«/mi»«/msup»«mo»-«/mo»«mn»1«/mn»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»2«/mn»«mi»n«/mi»«/msup»«/math» C.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»2«/mn»«mi»n«/mi»«/msup»«mo»+«/mo»«mn»1«/mn»«/math» D.None of these
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14.  If . nP3: nP2 =3:1, then n is equal to
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15.  The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs is
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16.  The letters of the words CALCUTTA and AMERICA are arranged in all possible ways. The ratio of the number of there arrangements is
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17.  In nPr ,n is always 
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18.  8 points are marked on the circumference of a circle. The number of chords obtained by joining these in pairs is
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19.  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mn»2«/mn»«mi»n«/mi»«mo»)«/mo»«mo»!«/mo»«/math» can be written as Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»2«/mn»«mi»n«/mi»«/msup»«mo»{«/mo»«mn»1«/mn»«mo».«/mo»«mn»3«/mn»«mo».«/mo»«mn»5«/mn»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»(«/mo»«mn»2«/mn»«mi»n«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»}«/mo»«mi»n«/mi»«mo»!«/mo»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»2«/mn»«mi»n«/mi»«/msup»«mi»n«/mi»«mo»!«/mo»«/math» C.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»{«/mo»«mn»1«/mn»«mo».«/mo»«mn»3«/mn»«mo».«/mo»«mn»5«/mn»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»(«/mo»«mn»2«/mn»«mi»n«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»}«/mo»«/math» D.None of these
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20.  The number of ways in which 9 things can be divided into twice groups containing 2, 3, and 4 things respectively is
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