Topic - Combinations MATHS RANKER DPP-3

1. (i) In how many ways can a team of 11 be chosen from 14 football players if two of them can be
only goalkeepers?
(ii) In how many ways can one select a cricket team of eleven from 17 players in which only 5
players can bowl if each cricket team of 11 must include exactly 4 bowlers.
2. To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the
vacancies are reserved for scheduled caste candidates while the rest are open to all, find the
number of ways in which the selections can be made.
3. (i) A committee consisting of 2 men and 2 women is to be chosen from 5 men and 6 women. In
how many ways can this be done?
(ii) A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how
many ways can this be done? How many of these committees would consist of 1 man and 2
women?
4. (i) There are 6 boys and 3 girls in a class. An entertainment committee of 6 persons is to be
selected such that there are 4 boys and 2 girls in the committee. In how many ways can the
committee be selected?
(ii) How many different committees each consisting of 3 girls and 2 boys can be chosen from 7
girls and 5 boys?
5. What is the number of ways of choosing 4 cards form a pack of 52 playing cards? In how many
of these:
(i) Four cards are of the same suit?
(ii) Four cards belong to four different suits?
(iii) Are face cards?
(iv) Two are red cards and two are black cards?
(v) Cards are of the same colour?
6. A bookshelf contains 7 different mathematics textbooks and 5 different physics textbooks. How
many groups of 3 mathematics and 3 physics textbooks can be selected?
7. Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if
each selection consists of 3 balls of each colour.
8. In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
9. A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red
balls can be selected from lot.
10. A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done
when the committee consists of at most 3 girls?
11. At an election three wards of a town are convassed by 4, 5 and 8 men respectively. If there are
20 volunteers. In how many ways can they be allotted to different wards?
12. Out of 7 men and 4 ladies a committee of 5 is to be formed. In how many ways can this be done
so as to include at least 3 ladies?
13. A candidate is required to answer six out of ten questions which are divided into two groups,
each containing five questions and he is not permitted to attempt more than 4 from any group.
In how many ways can he make up his choice?
14. A mathematics paper consists of 10 questions divided into two parts 1 and cach part containing
5 questions. A student is required to attempt 6 questions all, taking at least 2 questions from
each part. In how many ways can the student select the questions?
15. In an examination, a question paper consists of 12 questions divided into two parts 1 and II,
containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all,
selecting at least 3 from each part. In how many ways can a student select the questions?
16. There are 10 professors and 20 students out of whom committee of a 2 professors and 3 students
is to be formed. Find in how many ways these committee can be formed if
(i) a particular professor is included ? (ii) a particular professor is excluded ?
17. From 6 boys and 7 girls a committee of 5 is to be formed so as to include at least one girl. Find
the number of ways in which this can be done.
18. From 6 gentlemen and 4 ladies, a committee of 5 is to be formed. In how many ways can this be
done if
(i) There is no restriction?
(ii) The committee is to include at least one lady?
19. From 8 gentlemen and 4 ladies, a committee of 5 is to be formed. In how many ways can this be
done so as to include at least one lady?
20. In a group of 15 boys, there are 6 hockey players. In how many ways can 12 boys be selected so
as to include at least 4 hockey players?
21. From 7 gentlemen and 4 ladies a committee of 5 is to be formed. In how many ways can this be
done so as to include at least one lady?
22. From 7 gentlemen and 5 ladies, a boat party of 5 is to be formed. In how many ways can this be
done so as to include at least one lady?
23. A committee of 6 is to be formed out of 4 boys and 6 girls. In how many ways can it be done so
that the girls may not be outnumbered?
24. A person has 12 friends of whom 8 are relatives. In how many ways can he invite 7 friends such
that at least 5 of them may be relatives?
25. A candidate is required to answer 7 questions out of 12 questions which are divided into two
groups, each containing 6 questions. He is not permitted to attempt more than 5 from either
group. In how many different ways can he choose the seven questions?
26. Each of two parallel lines has a number of distinct points marked on them. On one line there are
2 points P and Q and on the other there are 8 points:
(i) Find the number of triangles formed having three of the 10 points as vertices.
(ii) How many of these triangles include P but exclude Q?
27. There are 7 men and 3 ladies contesting for two vacancies; an elector can vote for any number
of candidates not exceeding the number of vacancies. In how many ways can he vote ?
28. A party of 6 is to be formed from 10 boys and 7 girls so as to include 3 boys and 3 girls. In how
many different ways can the party be formed if two particular girls refuse to join the same party?
29. In an examination, the question paper contains three different sections A, B and C containing 4,
5 and 6 questions respectively. In how many ways, a candidate can make a selection of 7
questions, selecting at least two questions from each
Answer key
section.
1. (i) 132 (ii) 3960
5
2. C3 × C9× C4× 20C8× 5C5× 20C7
20 5

3. (i) 150 (ii) 10; 6

4. (i) 45 (ii) 350
5. 270725 (i) 2860 (ii) 134 (iii) 495
(iv) 105625 (v) 26900
6. 350
7. 2000
8. 40
9. 200
10. 1632
20
11. C4× 16C5× 11C8
12. 91
13. 200
14. 200
15. 420
16. (i) 1C1× 9C1× 20C3 (ii) 9C2× 20C3
7
17. C1× C4× C2× C3× C3× 6C2× 7C4× 6C1× 7C5× 6C0 or 12C5
6 7 6 7

- 6C5
18. (i) 252 (ii) 246
19. 736
20. 435
21. 441
22. 771
4
23. C3× 6C3× 4C2× 6C4× 4C1× 6C5× 6C6 = 195
24. 456
25. 780
26. (i) 64 (ii) 28
27. 55
28. 3600
29. 2700

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