Permutations & Combinations

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Q1. How many ways can 3 red balls and 2 blue balls be arranged in a line? (2016)

Solution:

The number of arrangements is 5! / (3! * 2!) = 10.

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Q2. 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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Q3. How many ways can 2 students be selected from a group of 5? (2019)

Solution:

The number of ways to select 2 students from 5 is given by 5C2 = 10.

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Q4. In how many ways can 3 different trophies be arranged on a shelf?

Solution:

The number of arrangements is 3! = 6.

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Q5. How many ways can 2 boys and 3 girls be selected from 5 boys and 6 girls?

Solution:

The number of ways is 5C2 * 6C3 = 10 * 20 = 200.

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Q6. In how many ways can 6 different colored balls be arranged in a row? (2018)

Solution:

The number of arrangements of 6 distinct balls is 6! = 720.

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Q7. How many ways can 6 people be selected from a group of 10? (2020)

Solution:

The number of ways to select 6 from 10 is C(10, 6) = 210.

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Q8. 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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Q9. How many ways can 4 different flags be arranged on a pole? (2021)

Solution:

The number of arrangements of 4 distinct flags is 4! = 24.

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Q10. How many ways can 4 different fruits be selected from 6 available fruits? (2021)

Solution:

The number of ways to choose 4 fruits from 6 is C(6, 4) = 15.