Permutations & Combinations

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Q1. How many different ways can 3 boys and 2 girls be seated in a row?

Solution:

The number of ways to arrange 5 people is 5! = 120.

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Q2. How many ways can 4 students be selected from a group of 12? (2014)

Solution:

The number of ways to select 4 students from 12 is given by 12C4 = 495.

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Q3. How many ways can 6 different flags be arranged on a pole? (2023)

Solution:

The number of arrangements of 6 different flags is 6! = 720.

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Q4. In how many ways can 3 different fruits be selected from a basket of 7 fruits? (2014)

Solution:

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

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Q5. How many different ways can 6 people be seated in a row? (2020)

Solution:

The number of arrangements of 6 people is 6! = 720.

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Q6. How many ways can 6 different books be arranged on a shelf? (2017)

Solution:

The number of arrangements of 6 different books is 6! = 720.

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Q7. How many ways can 4 different letters be chosen from the word 'COMPUTE'? (2022)

Solution:

The number of ways is 8C4 = 70.

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Q8. In how many ways can 4 different prizes be distributed among 10 students? (2023)

Solution:

The number of ways to distribute 4 different prizes among 10 students is 10P4 = 5040.

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Q9. How many ways can 2 boys and 3 girls be selected from 8 boys and 6 girls?

Solution:

The number of ways is 8C2 * 6C3 = 28 * 20 = 560.

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Q10. How many ways can 4 letters be chosen from the word 'COMBINATION'?

Solution:

The number of ways to choose 4 letters from 11 is 11C4 = 330.