Permutations & Combinations

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Q1. In how many ways can 4 different fruits be selected from 10 fruits?

Solution:

The number of ways to choose 4 fruits from 10 is C(10, 4) = 210.

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Q2. How many ways can 3 students be selected from a group of 10?

Solution:

The number of ways to select 3 students from 10 is given by 10C3 = 120.

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Q3. How many different ways can the letters of the word 'BOOK' be arranged? (2014)

Solution:

The number of arrangements of the letters in 'BOOK' is 4! / 2! = 12.

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Q4. How many different ways can 4 prizes be distributed among 10 students? (2020)

Solution:

The number of ways to distribute 4 prizes among 10 students is 10P4 = 10! / (10-4)! = 5040.

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Q5. In how many ways can 5 different colored balls be arranged in a line?

Solution:

The number of ways to arrange 5 different colored balls is 5! = 120.

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Q6. In how many ways can 7 people be divided into 3 groups if one group must have 3 people?

Solution:

Choose 3 people from 7: C(7, 3) = 35. The remaining 4 can be divided into 2 groups in 2 ways. Total = 35 * 2 = 70.

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Q7. How many ways can 3 different books be chosen from a set of 7?

Solution:

The number of ways to choose 3 from 7 is C(7, 3) = 35.

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Q8. In how many ways can 4 students be seated in a row of 6 chairs? (2021)

Solution:

Choose 4 chairs from 6 (6C4) and arrange 4 students (4!). Total = 15 * 24 = 360.

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Q9. How many ways can 5 different colored balls be arranged in a line? (2016)

Solution:

The number of arrangements of 5 different colored balls is 5! = 120.

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Q10. How many ways can a committee of 4 be formed from 10 people? (2019)

Solution:

The number of ways to form a committee of 4 from 10 is given by 10C4 = 210.