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Permutations and Combinations

The document contains a series of problems related to permutations and combinations, focusing on arrangements of letters and digits, formation of numbers, and selection of committees. It includes various scenarios such as avoiding adjacent letters, ensuring certain digits are used, and including specific gender compositions in committees. The problems are designed for Class XI students to practice and enhance their understanding of combinatorial mathematics.

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31 views1 page

Permutations and Combinations

The document contains a series of problems related to permutations and combinations, focusing on arrangements of letters and digits, formation of numbers, and selection of committees. It includes various scenarios such as avoiding adjacent letters, ensuring certain digits are used, and including specific gender compositions in committees. The problems are designed for Class XI students to practice and enhance their understanding of combinatorial mathematics.

Uploaded by

aksharanasrapally.arn
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Class-XI Permutations and combinations

1. In how many ways can the letters of the word ‘ARRANGE’ be arranged such that the two R’s do
not occur together.
2. How many 9-digit numbers of different digits can be formed
3. How many four digit even integers can be formed using the digits 0,1,2,3,4,5
4. How many 2-digit numbers can be formed from the digits 8,1,3,5and 4 assuming
(a) Repetition of digits is allowed (b)Repetition of digits is not allowed
5. From the digits 1,2,3,4,5,6, how many three digit odd numbers can be formed when the repetition
of the digits is not allowed
6. (i) How many different words can be formed with the letters of the word “BHARAT”
(ii) In how many of these B and H are never together
(iii) How many of these begin with B and end with T
7. (i) How many different arrangements can be formed with the letters of the word
“MATHEMATICS”
(ii) In how many of them vowels occur together
8. In how many ways can the letters of the word “COMBINE” be arranged so that
(i) The vowels are never separated
(ii) All the vowels never come together
(iii) Vowels occupy only odd places
9. There are 5 blue balls and 3 green balls. In how many ways they can be arranged in a row so that
no two green balls are together
10. How many add numbers less than 1000 can be formed using the digits 0,2,5,7 where
(i) Repetition is allowed (ii) Repetition not allowed
11. Ten different books are arranged on a shelf. Find the number of different ways in which this can be
done, if two specified books are (a) together (b) not together
12. In how many ways can 20 books be arranged on a shelf so that a particular pair of books shall not
come together
13. If (a) 4 P =n ( 4C ) , find n
2 2
(b) nC :nC =1:2 and nC : nC =2 :3 find the values of n and r
r r +1 r+1 r+ 2

14. A committee of 4 is to be selected from amongst 5 boys and 6 girls. In how many ways can this be
done so as to include at least one girl
15. How many different words, each containing 2 vowels and 3 consonants, can be formed with 5
vowels and 17 consonants
16. Find the number of (a) combinations,(b) permutations of four letters taken from the word
EXAMINATION
17. In how many ways can we a cricket eleven from 17 players in which 5 players can bowl, if each
cricket team should include 2 bowlers
18. A committee of 5 is to be formed from a group of 12 students consisting of 8 boys and 4 girls. In
how many ways can the committee be formed if it
(i)Consists of exactly 3 boys and 2 girls (ii) contains at least 3 girls
19. A committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many
ways can this be done if the committee includes at least one lady
20. Out of 3 books on Economics, 4 books on Political Science and 5 books on Geography, how many
collections can be made, if each collection consists of
(i)Exactly one book of each subject (ii) at least one book of each subject

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