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Discrete Mathematics | Basic Counting Principles MCQs

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

1. Suppose that E is capable of occurring m ways, while F is capable of occurring n ways. If both would not be possible simultaneously, then either E or F will be capable of occurring ___ times?

  1. m * n
  2. m + n
  3. m / n
  4. m - n

Answer: B) m + n

Explanation:

Suppose that E is capable of occurring m ways, while F is capable of occurring n ways. If both would not be possible simultaneously, then either E or F will be capable of occurring m + n times.


2. A student can choose a professor in __ ways if there are 8 female professors and 5 male professors teaching DAA?

  1. 5
  2. 8
  3. 13
  4. 40

Answer: C) 13

Explanation:

A student can choose a professor in 13 ways if there are 8 female professors and 5 male professors teaching DAA.


3. If we take the event E as having m possible ways to occur, and let us take a second event F as having n possible ways to occur, then combinations of both events can be produced with __ possible combinations?

  1. m/n
  2. mn
  3. mm
  4. nn

Answer: B) mn

Explanation:

If we take the event E as having m possible ways to occur, and let us take a second event F as having n possible ways to occur, then combinations of both events can be produced with mn possible combinations.


4. Students can choose a class monitor in ___ ways if there are 8 boys and 8 girls in the class?

  1. 8
  2. 16
  3. 32
  4. 64

Answer: D) 64

Explanation:

Students can choose a class monitor in 8 x 8 = 64 ways if there are 8 boys and 8 girls in the class.


5. In mathematics, the product of the first n natural numbers is known as ___ n?

  1. Factorial
  2. Binomial
  3. Multiplier
  4. Coefficient

Answer: A) Factorial

Explanation:

In mathematics, the product of the first n natural numbers is known as factorial n.


6. Factorial n is denoted by -?

  1. !n
  2. n!
  3. n|
  4. |n

Answer: B) n!

Explanation:

Factorial n is denoted by n!.


7. n! means -?

  1. n
  2. 2
  3. n (n-1) (n-2)...1
  4. n (n-1) (n-2)...2

Answer: C) n (n-1) (n-2)...1

Explanation:

n! Means n (n-1) (n-2)...1.


8. 0! is -?

  1. 0
  2. 1
  3. 2
  4. Infinite

Answer: B) 1

Explanation:

0! = 1


9. 5! is -?

  1. 5
  2. 20
  3. 0
  4. 120

Answer: D) 120

Explanation:

5! = 5 (5-1) (5-2) (5-3) (5-4) (5-5) = 5x4x3x2x1 = 120.


10. 5! / 3! is -?

  1. 666…
  2. 120
  3. 20
  4. Null

Answer: C) 20

Explanation:

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


11. If r and n are +ve integers and r ≤ n, then Binomial Coefficient is represented by - ?

  1. nCr
  2. rCn
  3. nPr
  4. rPn

Answer: A) nCr

Explanation:

If r and n are +ve integers and r ≤ n, then Binomial Coefficient is represented by nCr.


12. nCr means -?

  1. n (n-1) (n-2)...(n-r+1) / 1.2.3…(r-1) r
  2. 2.3…(r-1) r / n (n-1) (n-2)...(n-r+1)
  3. n (n-1) (n-2)...1 / 1.2.3…(r-1) r
  4. n (n-1) (n-2)...(n-r+1) / 1.2.3…(n-r+1) r

Answer: A) n (n-1) (n-2)...(n-r+1) / 1.2.3…(r-1) r

Explanation:

nCr means n (n-1) (n-2)...(n-r+1) / 1.2.3…(r-1) r.


13. 5C2 is -?

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

Answer: B) 10

Explanation:

5C2 = 5! / 2! . 3! = 5 x 4 x 3! / 2! . 3! = 5 x 4 / 1 x 2 = 20 / 2 = 10.





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