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Discrete Mathematics | Permutation and Combinations MCQs

Discrete Mathematics | Permutation and Combinations MCQs: This section contains multiple-choice questions and answers on Permutation and Combinations in Discrete Mathematics.
Submitted by Anushree Goswami, on July 20, 2022

1. The process of arranging n objects in a particular order is known as ___ of objects?

1. Permutation
2. Combination
3. Both A and B
4. None of the above

Answer: A) Permutation

Explanation:

The process of arranging n objects in a particular order is known as permutation of objects.

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2. A permutation of n objects taken r at a time is known as _____ taken in a given order?

1. r-permutation
2. Permutation of r objects
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

A permutation of n objects taken r at a time is known as an r-permutation or as a permutation of r objects taken in a given order.

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3. Permutation of r and n +ve integers where r ≤ n is denoted by -?

1. P (n, r)
2. P (r, n)
3. C (n, r)
4. C (r, n)

Answer: A) P (n, r)

Explanation:

Permutation of r and n +ve integers where r ≤ n is denoted by P (n, r).

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4. P (n,r) means -?

1. n! / r!
2. n! / (n! - r!)
3. n! / (n - r)!
4. r! / n!

Answer: C) n! / (n - r)!

Explanation:

P (n,r) means n! / (n - r)!.

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5. When n different objects are taken r at a time, the number of permutations in which p particular objects are not encountered is ____?

1. N - pr
2. N - p
3. N - r
4. n - Pp_r

Answer: D) n - Pp_r

Explanation:

When n different objects are taken r at a time, the number of permutations in which P particular objects are not encountered is n - Pp_r.

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6. When p particular objects are present at the same time, ____ is the number of permutations of n different objects taken at the same time?

1. n - Pp_r-p xRp_p
2. n - Pp_r-p xRp_r
3. n - Pp_r xRp_p
4. n - Pp_p xRp_r

Answer: A) n - Pp_r-p xRp_p

Explanation:

When p particular objects are present at the same time, n - Pp_r-p xRp_p is the number of permutations of n different objects taken at the same time.

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7. ____ permutations are those that are carried out around a circle?

1. Round
2. Circular
3. Global
4. Spherical

Answer: B) Circular

Explanation:

Circular permutations are those that are carried out around a circle.

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8. The order of the objects in a ____ does not matter, since it may contain some or all of the objects from a given set?

1. Permutation
2. Combination
3. Binomial
4. Boolean

Answer: B) Combination

Explanation:

The order of the objects in a Combination does not matter, since it may contain some or all of the objects from a given set.

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9. In ____, n objects are taken r at a time in combinations of r objects?

1. ^rC_n
2. ⁿC_r
3. ⁿC_r-1
4. ^n-1C_r

Answer: B) ⁿC_r

Explanation:

In ⁿC_r, n objects are taken r at a time in combinations of r objects.

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10. Combination of n objects, taken r at a time, is represented by -?

1. ⁿC_r
2. C (n,r)
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

Combination of n objects, taken r at a time, is represented by -

1. ⁿC_r
2. C (n,r)

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11. ⁿC_r means -?

1. n! / r! (n-r)!
2. n! / r!
3. n! / r! (r-n)!
4. r! / n!

Answer: A) n! / r! (n-r)!

Explanation:

ⁿC_r means n! / r! (n-r)!

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12. ⁵P₂ is -?

1. 5
2. 10
3. 20
4. 120

Answer: C) 20

Explanation:

⁵P₂ = 5! / 3! = 5 . 4 . 3! / 3! = 5 . 4 = 20.

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