Basic Concepts Of Permutations And Combinations

20 Questions  I  By Sweetsalman123
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1.  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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B.
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D.
2.  The number of different factors the number 75600 has is
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B.
C.
D.
3.  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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4.  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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B.
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D.
5.  The number of ways in which 6 men can be arranged in a row so that the particular 3 men sit together,is Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»4«/mn»«mi»P«/mi»«/msub»«mn»4«/mn»«/msub»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»4«/mn»«mi»P«/mi»«/msub»«mn»4«/mn»«/msub»«mo»§nbsp;«/mo»«mo»§#215;«/mo»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»3«/mn»«mi»P«/mi»«/msub»«mn»3«/mn»«/msub»«/math» C.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mn»3«/mn»«mo»!«/mo»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math» D.None of these
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6.  «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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7.  If 18C = 18C+2, the value of rC5 is
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8.  The Supreme Court has given a 6 to 3 decision upholding a lower court; the number of mays it can give a majority decision reversing the lower court is
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9.  0! is a symbol equal to
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10.  The value of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»12«/mn»«mi»c«/mi»«/msub»«mn»4«/mn»«/msub»«mo»+«/mo»«msub»«mn»12«/mn»«msub»«mi»c«/mi»«mn»3«/mn»«/msub»«/msub»«/math»
A.
B.
C.
D.
11.  «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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12.  The value of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mi»r«/mi»«mo».«/mo»«/mrow»«mrow»«mi»r«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mn»10«/mn»«/munderover»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»r«/mi»«msub»«mi»p«/mi»«mi»r«/mi»«/msub»«/msub»«/math» Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»11«/mn»«mi»P«/mi»«/msub»«mn»11«/mn»«/msub»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»11«/mn»«mi»P«/mi»«/msub»«mn»11«/mn»«/msub»«/math»-1 C.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»11«/mn»«mi»P«/mi»«/msub»«mn»11«/mn»«/msub»«/math»+1 D.None of these
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13.   If 5Pr= 60, then the value of r is
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D.
14.  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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15.  If . nP3: nP2 =3:1, then n is equal to
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D.
16.  The number of 4 digit numbers greater than 5000 can be formed out of the digits 3, 4, 5, 6 and 7 (no. digit is repeated). The number of such is
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D.
17.  If 12 school teams are participating in a quiz contest, then the number of ways the first, second and third positions may be won is
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18.  «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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D.
19.  There are 10 trains plying between Calcutta and Delhi. The number of ways in which a person can go from Calcutta to Delhi and return by a different train is 
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20.  The number of ways in which a person can chose one or more of the four electa appliances : T.V, Refrigerator, Washing Machine and a cooler is
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D.
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