Permutation and Combination

Q1) There are 5 seats available in a car. In how many ways can they five people be seated if only two can drive.
1) 72
2) 24
3) 48
4) 64

Solution:

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Q2) A multiple choice exam contains 5 questions, each having 4 possible answers. How many different ways are there to complete the exam?
1) 4⁵
2) 5⁴
3) 5⁵
4) 20

Solution:

Formation of words with Given Letters:

Number of permutations of 'n' objects out of which p are alike and are of one type, q are alike and are of second type and r are alike and are of third type

Download: Seating Arrangement around Geometrical Figures

Example:How many different words with or without meaning can be formed by using all the letters of the word ‘DIRECTOR’?

Solution: Total number of letters = 8. Here, R occurs 2 times.
Total number of arrangements =

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Q3 How many different words with or without meaning can be formed by using all the letters of the word ‘MATHEMATICS’.
1)
2)
3)
4)

Solution:

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Q4) If you have 7 books, in how many ways can you select five books and arrange them on a shelf?
1) 120
2) 5040
3) 21
4) 2520

Solution:

Q5) An unbiased coin is tossed 5 times. How many different outcomes have exactly 3 tails?
1) 3
2) 10
3) 6
4) 60

Solution:

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Q6) An unbiased coin is tossed 5 times. How many different outcomes have atmost 2 heads?
1) 15
2) 64
3) 10
4) 16

Solution:

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Q7) A bag contains 6 red and 4 black balls. In how many ways can we withdraw 5 balls out of which 3 are red?
1) 120
2) 20
3) 252
4) None of these

Solution:

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Q8) 8 friends have to be seated in a row for a group photo. In how many ways can they be seated in a row so that a particular person is always to the left of A.
1) 20160
2) 5040
3) 10080
4) 2520

Solution:

Q9) Six friends go to watch a movie. In how many ways can they be seated in a row of six seats so that three of them are always together.
1) 120
2) 720
3) 36
4) 144

Solution:

Download: Permutation and Combination Practice Questions

Q10) A bag contains 8 apples out of which 3 apples are rotten. In how many ways can you select a sample of 4 apples out of which at least 1 apple and at most 2 apples are rotten.
1) 65
2) 60
3) 56
4) 70

Solution: