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Permutation and Combination Questions

Permutation and Combination - Aptitude

1.Find the value of ⁶⁰P₃

x

Option: D

Explanation

⁶⁰P₃ = 60!/(60 - 3)!= 60!/57! = (60 * 59 * 58 * 57!)/57! = 60 * 59 * 58 = 205320

✉ Answer

2.Find the value of ¹⁰C₃

x

Option: A

Explanation

¹⁰C₃ = (10 * 9 * 8)/(3 * 2 * 1) = 120

✉ Answer

3.How many words can be formed by using all letters of the word 'BIHAR'?

x

Option: D

Explanation

BIHAR contains 5 different letters

Required number of words = ⁵P₅ = 5! = 5 * 4 * 3 * 2 * 1 = 120

✉ Answer

4.How many letters can be formed from the letters of the word 'DIRECTOR' so that the vowels are always together?

x

Option: A

Explanation

in the given word, treat the vowels IEO as one letter

thus, we have DRCTR (IEO)

this word has 6 letters of which R occurs 2 times and others are different

number of ways of arranging these letters = 6!/2! = 360

now 3 vowels can be arranged among themselves in 3! = 6 ways

required number of ways = (360 * 6) = 2160

✉ Answer

5.In how many ways can a cricket eleven be chosen out of a batch of 15 players?

x

Option: A

Explanation

required number of ways = ¹⁵C₁₁=¹⁵C_{15 - 11} = ¹⁵C₄

=(15 * 14 * 13 * 12)/(4 * 3 * 2 * 1) = 1365

✉ Answer

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