1.A cricket team of 11 players is to be selected from a group of 15 players of whom 5 are bowlers, 7 are batsmen and 3 are all-rounders. In how many ways can the team be selected so that it should contain 3 bowlers, 6 batsmen and 2 all-roundrs?
A.105
B.210
C.420
D.540
E.600
2. In how many ways can 7 letters be posted in 3 letter boxes
A.3
B.7
C.21
D.73
E.37
3.A plane contains 10 points in which no three poins are collinear.How many triangles can be formed using these points?
A.30
B.10c3
C.10p3
D.310
E.103
4. If 10c3=10cr, then what are the possible values of r?
A.3
B.4
C.5
D.6
E.7
F.8
G.9
5.A bag contains 5 red balls, 3 yellow balls and 2 white ball. The number of ways in which one or more balls can be taken out is
6. Mike attempts a true or false question paper which contains 5 questions at random. The number of ways he could have answered one or more questions is
A.9
B.10
C.24
D.31
E.32
7. Rohan has 6 friends whom he wants to invite for dinner. The number of ways in which he can invite atleast 1 of them are
A.1
B.6
C.21
D.31
E.32
F.63
G.64
8. In how many ways can three persons be seated in five chairs?
A.3
B.5
C.10
D.15
E.60
9. A cultural committee of 8 is to be formed from 9 Asians and 5 africans. In how many ways can it be done when the committee consists of exactly three africans?
A.8
B. 72
C.360
D.1260
E.1500
10.In how many ways can a committee of 6 can be formed from 10 members so that one particular person is always included and two particular persons ar never included?
A.10c6
B.9c6
C.9c5
D.8c6
E.7c2
F.7c3
G.7c5
11. If nc5 =nc3, find 10cn
| COLUMN A | COLUMN B<> |
| nc0 | np0 |
A. If column A is greater
B. If column B is greater
C. Both are equal
D. Cannot be determined
13.When 5 coins are thrown in how many ways it show exactly three tails?
A. 1
B. 3
C. 5
D. 10
E. 15
14.There are 12 points in a plane in which 7 points are collinear. How many straight lines can be formed by joining these points?
A. 12c2
B. 7c2
C. 12c2-7c2
D. 12c2-7c2+1
E. 12-7+1
15. There are 12 points in a plane in which 7 points are collinear. How many straight triangles can be formed by joining these points?
A. 12c3
B. 7c3
C. 12c3-7c3
D. 12c3-7c3+1
E. 12c3+7c3+1
16. A number plate should have four digits.If the first digit is three, the second digit is a positive even number and the last two digits are in ascending order, then find the total number of different number plates possible.
A. 120
B. 135
C. 144
D. 180
E. 225
17. In how many ways can six students and six teachers sit around a circular table so that no two students are sitting together?
A. 5!5!
B. 5!6!
C. 6!6!
D. 11!
E. 12!
18.
| COLUMN A | COLUMN B |
| The number of ways it can show atleast 1 head | The number of ways it can show atleast 1 tail |
A. If column A is greater
B. If column B is greater
C. Both are equal
D. Cannot be determined
19. When two dice are thrown the number of ways it show sum atleast 11?
A. 1
B. 2
C. 3
D. 4
E. 5
20. The number of diagonal in a 12 sided polygon is
A. 6
B. 9
C. 27
D. 54
E. 108
1.A cricket team of 11 players is to be selected from a group of 15 players of whom 5 are bowlers, 7 are
batsmen and 3 are all-rounders. In how many ways can the team be selected so that it should contain 3 bowlers, 6 batsmen and 2 all-roundrs?
6 batsmen can be selected from 7 in 7c6 ways
2 all-rounders can be selected from 3 in 3c2 ways
5c3x7c6x3c2
=10x7x3=210.
In how many ways can 7 letters be posted in 3 letter boxes
first letter can be posted in 3 wayssecond letter can be posted in 3 ways
third letter can be posted in 3 ways
fourth letter can be posted in 3 ways and so on
seventh letter can be posted in 3 ways
the answer is 3x3x3x3x3x3x3 ways.
37 is the answer.
A plane contains 10 points in which no three poins are collinear.How many triangles can be formed using these points?
To form a triangle we require 3 points. It we have to select 3 points from 10 pointstherefore 10c3
If 10c3=10cr, then what are the possible values of r?
we knoe that ncr=ncn-r10c3=10cr
r=3 or (10-3)
A bag contains 5 red balls, 3 yellow balls and 2 white ball. The number of ways in which one or more balls can be taken out is
5 red balls can be choosen in 6 ways (0,1,2,3,4,5)3 yellow balls can be choosen in 4 ways (0,1,2,3)
2 white balls can be choosen in 3 ways (0,1,2).
The no of ways possible is 6x4x3=72
atleast one ball means 72-1=71.
6. Mike attempts a true or false question paper which contains 5 questions at random. The number of ways he could have answered one or more questions is
Each question can be attempted in 2 ways so, 5 questions can be attempted in 25=32 ways.He has to attempt one or more questions in 32-1= 31 waysRohan has 6 friends whom he wants to invite for dinner. The number of ways in which he can invite atleast 1 of them are
He can invite his friends in 6c1+6c2+6c3+6c4+6c5+6c6=63 ways.In how many ways can three persons be seated in five chairs?
3 persons can be seated in 5 chairs in 5p3 ways.5x4x3=60 ways.
3 africans can be selected from 5 in 5c3=10 ways
5 asians can be selected from 9 in 9c5=126 ways
the answer is 10x126=1260 ways.
In how many ways can a committee of 6 can be formed from 10 members so that one particular person is always included and two particular persons ar never included?
We have to select 6 from 10. But numbers never be selected it means we have to select from 8.However one particular person is always included therefore we have to select 5 from 7In 7c5 ways
7c5=7c2.
If nc5 =nc3, find 10cn
we know that If ncr =ncn-rnc5 =nc3=> n=8
10c8=45.
| COLUMN A | COLUMN B<> |
| nc0 | np0 |
| COLUMN A | COLUMN B |
| The number of ways it can show atleast 1 head | The number of ways it can show atleast 1 tail |
When two dice are thrown the number of ways it show sum atleast 11?
sum atleast 11 means it can show 11 or 12the possible for 11 is (5,6) and (6,5)
the possible for 12 is (6,6)
The answer is 3 ways.
The number of diagonal in a 12 sided polygon is
The number of diagonal in a n sided polygon is n(n-3)/2.Therefore the required answer is 12(12-3)/2=54