Practice Questions 5-Permutation and Combination-Class XI
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Question 1 of 16
1. Question
1 point(s)Find the no. of words can be formed from the word “SUCCESSFUL’?
CorrectIncorrectHint
In ‘SUCCESSFUL’ there are 2 no. of C, 2 no. of S, 2 no. of U and there are total of 10 letters.
Total no. of words
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Question 2 of 16
2. Question
1 point(s)In how many different ways can the letter of the word ‘ELEPHANT’ be arranged so that vowels always occur together?
CorrectIncorrectHint
There are 8 letters in the word ‘ELEPHANT’ & 3 vowels E, E, A.
The vowels arranged themselves in
ways.
We can take all the vowels a single letter.
Since we have 5+1=6 no. of letters.
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Question 3 of 16
3. Question
1 point(s)There are 4 bananas, 7 apples & 6 mangoes in a fruit baskets. In how many ways can a person make a selection of fruits from the basket?
CorrectIncorrectHint
There are 4 bananas, 7 apples, 6 mangoes.
We make take 0 banana, 1 banana, 2 banana, 3 banana, 4 banana respectivaly for other fruits also.
Hence the total ways to selectings bananas, apples & mangoes is
ways.
Since we not conclude 0 no. of each fruits hence we subtract 1 ways.
Required no.of ways =280-1=279 -
Question 4 of 16
4. Question
1 point(s)There are 15 points in a plane out of which 6 are collinear. Find the no. of lines that can be formed from 15 points.
CorrectIncorrectHint
From 15 points no. of lines formed
6 points are collinear, no. of lines formed by these
Total lines 
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Question 5 of 16
5. Question
1 point(s)In how many ways 4 Indians, 5 Africans & 7 Japanese be seated in a row so that all person of same nationality sit together?
CorrectIncorrectHint
4 Indians seated in 4! ways.
5 Africans seated in 5! ways.
7 Japanese seated in 7! ways.
All three nationality seated in 3! ways.
Total no.of ways =(4!)(5!)(7!)(3!) -
Question 6 of 16
6. Question
1 point(s)In how many ways 5 americans & 5 Indians be seated along a circluar table, so that they are seated in alternative position?
CorrectIncorrectHint
Indian are seated in 5! ways.
Americans are seated in (5-1)!=4! ways.
Total no.of ways=(4!)(5!) -
Question 7 of 16
7. Question
1 point(s)4 matches are to be played in a chess tournament. In how many ways can result be decided?
CorrectIncorrectHint
Every chess match can have 3 result i.e. win, loss or draw.
So no.of ways
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Question 8 of 16
8. Question
1 point(s)A box cantain 20 balls. In how many ways can 8 balls be selected if each ball can be repeated any number of times?
CorrectIncorrectHint
Hence n=20, r=8
Required no. of ways
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Question 9 of 16
9. Question
1 point(s)There are 11 Players in a cricket squad which is to be sent to Australian tour i.e. The total no.of members are 15. If 2 particuar member is always included. How manys ways the players could selected in them?
CorrectIncorrectHint
Total no.of players=15
2 particular players are always included.
A squad contain 11 players.
Hence (15-2=13) players will be take part and (11-2=9) player are to be chosen.
No. of ways 
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Question 10 of 16
10. Question
1 point(s)A box contain 12 black balls, 7 red balls and 6 blue balls. In how many ways can one or more balls be selected?
CorrectIncorrectHint
There are 3 kind of balls.
Required no. of ways=(12+1)(7+1)(6+1)-1
=728-1=727 -
Question 11 of 16
11. Question
1 point(s)There are 12 copies of Mathematics, 7 copies Of Engineering, 3 different books on medicine & 2 different books on Economics. Find the no. of ways in which one on more than one book can be selected?
CorrectIncorrectHint
12 copies of Mathematics, 7 copies of Engineering, 3 different books from medicines & 2 different books of Economics.
If there are 5 different books.
Total no. of ways
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Question 12 of 16
12. Question
1 point(s)There are 10 different books & 20 copies of each book in a library. In how many ways can one or more than one book be selected?
CorrectIncorrectHint
There are 10 different books.
Each book has 200 copies & all the copipes of each particular book can be considered as identical.
Total no. of ways
![=[(20 + 1)(20 + 1)...(10times)] - 1](https://fosterjee.com/wp-content/ql-cache/quicklatex.com-40a1a98d4ddc72758e1d009a29b49804_l3.png "Rendered by QuickLaTeX.com")
![= [21 \times 21 \times ...(10times)] - 1](https://fosterjee.com/wp-content/ql-cache/quicklatex.com-8fe9defbfc1f8e7ceac88c8ea1b4119e_l3.png "Rendered by QuickLaTeX.com")
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Question 13 of 16
13. Question
1 point(s)In how many ways can 4 different balls be distruibuted among 5 different boxes when any box can have any no. of balls?
CorrectIncorrectHint
Hence n=5, k=4
Required no. of ways 
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Question 14 of 16
14. Question
1 point(s)In how many ways can 3 different balls be distruibuted among 2 different boxes when any box can have any no. of balls?
CorrectIncorrectHint
Hence n=2, k=3
required no. of ways 
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Question 15 of 16
15. Question
1 point(s)In how many ways can 5 distinguishable balls put into 8 disinguishable boxes if no box can contain more than one ball?
CorrectIncorrectHint
Hence n=8, k=5
Required no. of ways
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Question 16 of 16
16. Question
1 point(s)Find the value of m where \({}^8{P_3} = {}^8{C_{3 \times m}}\)
CorrectIncorrectHint
m=3!