CLASS XI PERMUTATION DPP
PERMUTATIONS
1. find the value 1) 2024C2 / 2023
2. find n If n(n-1)(n-2)(n-3)(n-4) / 5 = 24
3. find the value of 2024C0 + 2023C0 + 2022C0 + ... + 2C2 + 1C1
4. If 2024C2n+2 = 2024C8-k find k
5. If 17Cx-3 = 17C95 find x
6. If 59C32 = x + 59C27, find the value of 2n+3.
7. find the value of 2024C2022 / 2024C2
8. If 17C11 / 17C6 = x, then find the value of 14x-3.
9. If 17C11 + 17C12 = xC12 find the value of √2x.
10. If 15C9 + 15C10 = 16Ck find the sum of all possible value of k
11. find the value of 8C8 + 8C7 + ... + 8C1 + 8C0
12. find the value of 10C10 + 10C8 + 10C6 + 10C4 + 10C2
13. find the value of 2024C2024 + 2024C2022 + ... + 2024C0 / 2023C2023
+ 2023C2021 + 2023C2019 + ... + 2023C1
14. find the value of n If 100C0 + 100C1 + 100C2 + ... + 100C100 = 2n
✤ WORD PROBLEM
1. 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 questions from either group. Find
the number of different ways of doing questions.
2. On of 18 points in a plane, no three are in the same line except five
points which are collinear. Find the number of lines that can be formed
joining the points.
3. We wish to select 6 persons from 8, but if the person A is chosen then
B must be chosen. In how many ways can selections be made?
4. How many automobile license plates can be made if each plate contains
two different letters followed by three different digits?
5. Find the number of permutations of n distinct things taken together, in
which 3 particular things must occur together.
6. Find the number of positive integers greater than 6000 and less than
7000 which are divisible by 5, provided that no digit is to be repeated.
7. There are 10 persons named P₁, P₂, P₃....P₁₀. Out of 10 persons, 5
persons are to be arranged in line such that in each arrangement P₁
must occur whereas P₄ and P₅ do not occur. Find the number of such
possible arrangements.
8. There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be
illuminated.
9. A box contains two white, three black and four red balls. In how many
ways can three balls we drawn from the box, if atleast one black ball is
to be included in the draw.
10. Find the number of integers greater than 7000 then can be formed with
the digits 3,5,7,8 and 9 where no digit is repeated.
11. If 20 lines are drawn in plane such that no two of them are parallel and
no three are concurrent, in how many points will they intersect each
other?
12. In a certain city, all telephone numbers have six digits, the first two
digits always being 41 or 42 or 46 or 62 or 64. How many telephone
numbers have all six digits distinct?
13. In an examination, a student has to answer 4 questions out of 5
questions; questions 1 and 2 are however compulsory. Determine the
number of ways in which the student can make the choice.
14. 18 mice were placed in two experimental groups and one control
group, with all groups equally large. In how many ways can the mice be
placed into three groups?
15. A bag contains six white marbles and five red marbles. Find the number
of ways in which four marbles can be drawn from the bag if
(i) they can be of any colour
(ii) two must be white and two red and
(iii) they must all be of the same colour.
16. In how many ways can a football team of 11 players be selected from
16 players? How many of them will
(i) include 2 particular players?
(ii) exclude 2 particular players?
17. A sports team of 11 students is to be constituted, choosing at least 5
from Class XI and at least 5 from Class XII. If there are 20 students in
each of these classes, in how many ways can be the team be
constituted?
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 girls (ii) at least one boys and ane girl
(iii) at least three girls
19. How many numbers greater than 1000000 can be formed by using the
digits 1, 2, 0, 2, 4, 2, 4? [NCERT]
20. In how many ways can the letters of the word ASSASSINATION be
arranged so that all the S's are together? [NCERT]
21. Find the total number of permutations of the letters of the word
'INSTITUTE'. [NCERT]
✤ BASED ON LOTS
1. The letters of the word 'SURITI' are written in all possible orders and
these words are written out as in a dictionary. Find the rank of the word
'SURITI'.
2. In how many ways can the letters of the word 'ALGEBRA' be arranged
without changing the relative order of the vowels and consonants?
3. How many words can be formed with the letters of the word
'UNIVERSITY', the vowels remaining together?
4. Find the total number of arrangements of the letters in the expression
a³ b² c⁴ when written at full length.
5. How many words can be formed with the letters of the word
'PARALLEL' so that all L's do not come together?
6. How many words can be formed by arranging the letters of the word
'MUMBAI' so that all M's come together?
7. How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so
that the odd digits always occupy the odd places?
8. How many different signals can be made from 4 red, 2 white and 3
green flags by arranging all of them vertically on a flagstaff?
9. How many number of four digits can be formed with the digits 1, 3, 3,
0?
10. In how many ways can the letters of the word 'ARRANGE' be arranged
so that the two R's are never together?
11. How many different numbers, greater than 50000 can be formed with
the digits 0, 1, 1, 5, 9.
12. How many words can be formed from the letters of the word 'SERIES'
which start with S and end with S?
13. How many permutations of the letters of the word 'MADHUBANI' do
not begin with M but end with I?
14. Find the number of numbers, greater than a million, that can be formed
with the digits 2, 3, 0, 3, 4, 2, 3.
15. There are three copies each of 4 different books. In how many ways can
they be arranged in a shelf?
16. How many different arrangements can be made by using all the letters
in the word 'MATHEMATICS'. How many of them begin with C? How
many of them begin with T?
17. A biologist studying the genetic code is interested to know the number
of possible arrangements of 12 molecules in a chain. The chain
contains 4 different molecules represented by the initials A (for
Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3
molecules of each kind. How many different such arrangements are
possible?
18. In how many ways can 4 red, 3 yellow and 2 green discs be arranged in
a row if the discs of the same color are indistinguishable? [NCERT]
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