Basic Concepts Of Permutations And Combinations

20 Questions  I  By Sweetsalman123
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1.  The number of ways in which 9 things can be divided into twice groups containing 2, 3, and 4 things respectively is
A.
B.
C.
D.
2.  The number of ways in which 15 mangoes can be equally divided among 3 students is Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»15«/mn»«mo»!«/mo»«/mrow»«mrow»«mo»(«/mo»«mn»5«/mn»«msup»«mo»)«/mo»«mn»4«/mn»«/msup»«mo»!«/mo»«/mrow»«/mfrac»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»15«/mn»«mo»!«/mo»«/mrow»«mrow»«mo»(«/mo»«mn»5«/mn»«msup»«mo»)«/mo»«mn»3«/mn»«/msup»«mo»!«/mo»«/mrow»«/mfrac»«/math» C.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»15«/mn»«mo»!«/mo»«/mrow»«mrow»«mo»(«/mo»«mn»5«/mn»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«mo»!«/mo»«/mrow»«/mfrac»«/math» D.None of these
A.
B.
C.
D.
3.  The number of ways the letters of the word COMPUTER can be rearranged is
A.
B.
C.
D.
4.  If 18C = 18C+2, the value of rC5 is
A.
B.
C.
D.
5.  The total number of 9 digits numbers of different digits is
A.
B.
C.
D.
6.  7! is equal to
A.
B.
C.
D.
7.  The number of arrangement of the letters of the word COMMERCE is
A.
B.
C.
D.
8.  The number of numbers lying between 10 and 1000 can be formed with the digits 2,3,4,0,8,9 is
A.
B.
C.
D.
9.  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
A.
B.
C.
D.
10.  The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is
A.
B.
C.
D.
11.  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
A.
B.
C.
D.
12.  The number of ways in which 12 students can be equally divided into three groups is 
A.
B.
C.
D.
13.  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
A.
B.
C.
D.
14.  If nP4 = 12 x nP2, then is equal to 
A.
B.
C.
D.
15.  5 letters are written and there are five letter-boxes. The number of ways the letters can be dropped into the boxes, are in each
A.
B.
C.
D.
16.  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
A.
B.
C.
D.
17.  In a group of boys the number of arrangement of 4 boys is 12 times the number of arrangements of 2 boys.The number boys in the group is
A.
B.
C.
D.
18.  There are 12 points in a plane of which 5 are collinear. The number of triangles is
A.
B.
C.
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 
A.
B.
C.
D.
20.  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
A.
B.
C.
D.
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