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Permutations and Combinations Applied Maths - Permutations and Combinations

CBSE - STD 11 Science - Applied Maths (CBSE - English Medium). 50 questions in this chapter.

Question types

Permutations and Combinations question types

50 questions across 7 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.

50
Questions
7
Question groups
5
Question types
Sample Questions

Permutations and Combinations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
The number of ways in which a team of 11 players can be selected from 22 players always including 2 of them and excluding 4 of them is
  • A
    ${ }^{16} C_{11}$
  • B
    ${ }^{16} C_5$
  • ✓
    ${ }^{16} C_9$
  • D
    ${ }^{20} C_9$

Answer: C.

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Q 3MCQ1 Mark
The straight lines $l_1, l_2, l_3$ are parallel and lie in the same plane. A total number of $m$ points are taken on $l_1 ; n$ points on $l_2 ; k$ points on $l_3$, The maximum number of triangles formed with vertices at these points are
  • A
    ${ }^{(m+n+k)} C_3$
  • ✓
    ${ }^{(m+n+k)} C_3-{ }^m C_3-{ }^n C_3-{ }^k C_3$
  • C
    ${ }^m C_3+{ }^n C_3+{ }^k C_3$
  • D
    ${ }^m C_3 \times{ }^n C_3 \times{ }^k C_3$

Answer: B.

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Q 4MCQ1 Mark
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
  • A
    45
  • ✓
    350
  • C
    4200
  • D
    230

Answer: B.

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Q 5MCQ1 Mark
The sum of the digits in unit place of all the numbers formed with the help of $3,4,5$ and 6 taken all at a time is
  • A
    432
  • ✓
    108
  • C
    36
  • D
    18

Answer: B.

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Q 72 Marks Questions2 Marks
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?
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Q 102 Marks Questions2 Marks
In how many ways can a student choose a program of 5 courses, if 9 courses are available and 2 specific courses are compulsory for every student?
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Q 113 Marks Question3 Marks
Using the letters of the word 'ARRANGEMENT' how many different words (using all letters at a time) can be made such that both $A$, both $E$, both $R$ and both $N$ occur together.
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Q 153 Marks Question3 Marks
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.
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Q 175 Marks Questions5 Marks
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if a team has
(i) no girl
(ii) at least 3 girls
(iii) At least one boy and one girl
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Q 185 Marks Questions5 Marks
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 at a time.
(iii) all letters are used but first letter is a vowel.
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Q 195 Marks Questions5 Marks
In how many ways can be letters of the word PERMUTATIONS be arranged if the :
(i) Words start with $P$ and end with $S$,
(ii) Vowels are all together,
(iii) There are always 4 letters between $P$ and $S$ ?
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Q 205 Marks Questions5 Marks
In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back ? How many seating arrangements are possible if 3 girls should sit together in a back row on adjacent seats ?
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Q 21Fill in the blanks.1 Mark
Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if atleast 2 are red is _________________ .
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Q 22Fill in the blanks.1 Mark
Every body in a room shakes hand with everybody else. The total number of hand shakes is 66 . The total number of persons in the room is _________________ .
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Q 264 Marks Questions4 Marks
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. (iii) they must all be of the same colour.
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Q 274 Marks Questions4 Marks
From 6 different novels and 3 different dictionaries, 4 novels and a dictionary is to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then find the number of such arrangements.
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Q 304 Marks Questions4 Marks
A committee of 7 has to be formed out of 9 boys and 4 girls. In how many ways can be this be done when the committee consists of
(i) exactly 3 girls
(ii) At most 3 girls ?
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Q 31Match the following.4 Marks
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturers is to be formed. Find :
(a) In how many ways committee can be formed(i) ${ }^{10} C_2 \times{ }^{19} C_3$
(b) In how many ways a particular professor is included(ii) ${ }^{10} C_2 \times{ }^{19} C_2$
(c) In how many ways a particular lecturer is included(iii) ${ }^{9} C_1 \times{ }^{20} C_3$
(d) In how many ways a particular lecturer is excluded(i) ${ }^{10} C_2 \times{ }^{20} C_3$
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Q 32Match the following.4 Marks
Five boys and five girls form a line. Find the number of ways of making seating arrangements under the following conditions :
$C _1$$C _2$
(a) Boys and girls alternate(i) $5!\times 6$ !
(b) No two girls sit together(ii) $10!-5! 6$ !
(c) All the girls sit together(iii) $(5!)^2+(5!)^2$
(d) All the girls are never together(iv) $5!\times 6$ !
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