Basic Concepts Of Permutations And Combinations

20 Questions  I  By Sweetsalman123
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1.  If n cr-1 = 56, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mi»n«/mi»«mi»c«/mi»«/msub»«mi»r«/mi»«/msub»«/math»= 28 and n cr+1 = 8, then r is equal to
A.
B.
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D.
2.  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»
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B.
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D.
3.  10 examination papers are arranged in such a way that the best and worst papers never come together. The number of arrangements is
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D.
4.  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mn»4«/mn»«msub»«mi mathvariant=¨bold¨»P«/mi»«mn»4«/mn»«/msub»«/msub»«/math» is equal to
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D.
5.  The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3, 4, 5, 6, 7 is
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B.
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D.
6.  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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B.
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D.
7.  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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D.
8.  «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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B.
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D.
9.  The number of ways in which 7 boys sit in a round -table so that two particular boys may sit together is
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B.
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D.
10.  A committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 gents. Mrs. X refuses to serve in a committee in which Mr. Y is a member. The number of such committees is
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11.  If the letters word 'Daughter' are to be arranged so that vowels occupy the odd places, then number of different words are
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12.  3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is
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13.  If n1+n2 P2 = 132, n1-n2P2 = 30 then,  
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14.  There are 5 speakers A,B,C,D,E.The number of ways in which A will speak always before B is Options:  A.24 B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«mo»!«/mo»«mo»§#215;«/mo»«mn»2«/mn»«mo»!«/mo»«/math» C.5! D.None of these
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B.
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D.
15.  The number of ways in which 8 different beads be strung on a necklace is
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B.
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D.
16.  The number of ways in which the letters of the word DOGMATIC can be arranged is
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B.
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D.
17.  Mr. X and Mr. Y enter into a railway compartment having six vacant seats. The number of ways in which they can occupy the seats is
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18.  The number of ways in which 12 students can be equally divided into three groups is 
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D.
19.  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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B.
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20.  Lf 500 C92=499C92 + nC91 then x is
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D.
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