1.Algebra Booster

Permutations and Combinations 5.9
130. In how many ways, 20 different pearls of two colors
can be set alternately on a necklace, there being 10
pearls of each color?
131. How many necklace of 20 beads each can be made
from 10 beads of various colors?
COMBINATIONS
132. In how many ways, 7 different books be given to 2 students—one
gets 4 books and other gets 3 books?
133. In how many ways, Master Rohan can invites 4 friends
out of his 10 friends in a dinner?
134. In how many ways, I can select the best 5 mathematics
students out of 12 students for an Olympiad examination?
135. In how many ways, a team of 3 boys and 4 girls can be
selected out of 7 boys and 9 girls?
136. In how many ways, 5 vowels and 5 consonants can be
selected from 26 letters in the English alphabet?
137. If a bus conductor has 190 different tickets, find the
number of stoppage that the bus has consider only one
way journey?
138. On a new year day, every student of a class sends a card
to every other student. The postman delivers 600 cards.
How many students are there in the class?
139. A man has 10 children to take them in a circus. He
takes 4 of them at a time to the circus as often as he can
without taking the same 4 children together more than
once. How many times will he has to go to circus?
140. In an election, three wards of a town are canvassed by 4, 5
and 8 men, respectively. If there are 20 volunteers, in how
many ways can they have allotted to different wards?
141. In how many ways, 4 cards are choosing from a pack of
52 cards in which all are of the same suit?
142. In how many ways, 4 cards are choosing from a pack of
52 cards in which all are of different suits?
143. Out of 6 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 in each committee?
144. Find the domain of the function f(x) = 2x – 5 C x – 2
.
145. Find the range of the function f(x) = 3x – 7 C x – 1
.
146. If 10 C r
= 10 C r + 2
, find r.
147. If n C n – 4
= 15, find the value of n
148. If 15 C r
: 15 C r – 1
= 11 : 5, find r.
149. Find the value of
20
C 13
+ 20 C 15
+ 20 C 9
– 20 C 7
– 20 C 5
– 20 C 11
.
150. If n – 1 C 3
+ n – 1 C 4
> n C 3
, prove that n > 7.
5
47 52-
j
151. Find the value of C4+ Â C3.
j = 1
152. If n C r – 1
= 36, n C r
= 84 and n C r + 1
= 126, find n and r.
153. Solve for x: x + 3 P 3
= x + 2 C 3
+ 20.
154. If m = n C 2
, find the value of m C 2
.
1 1 1
155. If 4
= 5
+ 6 , find n.
Cn Cn Cn
RESTRICTED COMBINATIONS
156. In how many ways, can we select the best 20 students
for JEE-Advanced examination from a batch of 100
students, if
(i) two particular students are always chosen?
(ii) five particular students are never chosen?
157. A group of students consists of 4 boys and 5 girls. Find
the number of ways of selecting a team of at least 3
boys and 4 girls.
158. How many ways are there choosing a hand of 6 cards
containing an ace and a king of the same suit from a
pack of 52 cards?
159. 10 cards are taken out from a well-shuffle pack of 52
cards. In how many ways of choosing a hand of 10
cards consists of at least one ace?
160. A bag contains 5 black and 5 red balls, all balls being
different. Find the number of ways in which 2 black
and 3 red balls can be selected.
161. Out of 6 gentleman 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 in each committee?
162. 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 this can be done?
163. A candidate is required to answer 7 questions out of 12
questions, which are divided into two groups containing
6 questions each. He is not permitted to attempt
more than 5 from either group. In how many different
ways, can be chosen the seven questions?
164. 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 section.
165. In an election for 3 seats, there are 6 candidates. A voter
cannot vote for more than 3 candidates. In how many
ways can he vote?
COMBINATIONS FROM DISTINCT OBJECTS
166. Master Amit has 8 friends. In how many ways he can
invite one or more of them in his birthday?
167. In how many ways, Master Roshan can give answer
at least one question out of 10 questions in his class
test?
168. In an examination, a student will pass if he/she passes
all 5 subjects in his class. In how many ways he/she
will fail the examination?
169. A questions paper consists of two sections having 3 and
5 questions respectively. One question from each section
is compulsory. In how many ways can a student
select the question?
170. A bag contains 2 white and 3 red cubes, all of different
sizes. In how many ways can 3 cubes be selected from
the bag if