BGSIPS, CLASS-XI
MATHS WORKSHEET
CHAPTER- PERMUTATIONS AND COMBINATIONS
1. It is required to seat 5 men and 4 women in a row so that the women occupy the
even places. The number of ways such arrangements are possible are
(a) 8820
(b) 2880
(c) 2088
(d) 2808
2. How many 3-letter words with or without meaning, can be formed out of the letters
of the word, LOGARITHMS, if repetition of letters is not allowed
(a) 720
(b) 420
(c) none of these
(d) 5040
3. 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 least 3 girls
(a) 588
(b) 885
(c) 858
(d) None of these
4. Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels
and 5 consonants is equal to
(a) 60
(b) 120
(c) 7200
(d) 720
5. In how many ways can 12 people be divided into 3 groups where 4 persons
6. How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9
and 5 when repetition of digits is not allowed?
7. How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4,
5 while each digit may be repeated any number of times?
8. How many 3 digits number are there, with no digit repeated?
9. Evaluate the following: (i) 14 𝐶2 (ii) 35 𝐶35
10. If 18 𝐶𝑥 = 18 𝐶𝑥+2 , find 𝑥.
11. If 𝑛 𝐶4 , 𝑛 𝐶5 𝑎𝑛𝑑 𝑛 𝐶6 are in A.P., then find n.
12. How many words, with or without meaning can be made from the letters of the word
MONDAY. Assuming that no. letter is repeated, if
(i) 4 letters are used at a time
(ii) All letters are used but first letter is a vowel?
13. 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.
14. How many numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4,
2, 3?
15. How many committees of 5 persons with a chairperson can be selected from 12
persons?
16. In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are
together?
17. Find the number of diagonals of (i) hexagon (ii) a polygon of 16 sides
18. A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be
selected if the team has:
(i) no girl?
(ii) at least one boy and one girl?
(iii) at least 3 girls?
19. What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In
how many of there
(i) Four cards of the same suit
(ii) Four cards belong to four different suits
(iii) Are face cards.
(iv) Two are red cards & two are black cards.
(v) Cards are of the same colour?
20. If the letters of the word `MOTHER’ are written in all possible orders and these words
are written out as in a dictionary, find the rank of the word `MOTHER’.
21. A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this
can be done, when
(i) At least two ladies are included
(ii) At most two ladies are included
22. A sports team of 11 students is to be constituted, choosing at least 5 from Class XI and at
least from Class XII. If there are 20 students in each of these classes, in how many ways can
be the team be constituted?
23. From 7 consonants and 4 vowels, how many different words can be formed consisting of 3
consonants and 2 vowels?
24. In a small village, there are 87 families, of which 52 families have at most 2 children. In a
Rural Development Program, 20 families are to be chosen for assistance, of which at least 18
families must have at most 2 children. In how many ways can the choice be made?
