Permutation And Combination - Aptitude MCQ Questions and Solutions with Explanations

Permutation And Combination MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Permutation And Combination with easy and logical explanations. Permutation And Combination MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc. Page-7 section-2

In how many ways can a committee of 4 people be chosen out of 8 people?

A) 32 B) 70 C) 110 D) 126 E) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

Required number of ways
$$\eqalign{ & = {}^8{C_4} \cr & = \frac{{8 \times 7 \times 6 \times 5}}{{4 \times 3 \times 2 \times 1}} \cr & = 70 \cr} $$

In how many different ways can the letters of the word EXTRA be arranged so that the vowels are never together?

A) 120 B) 48 C) 72 D) 168 E) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

Taking the vowels (EA) as one letter, the given word has the letters XTR (EA), i.e., 4 letters.
These letters can be arranged in 4! = 24 ways
The letters EA may be arranged amongst themselves in 2 ways.
Number of arrangements having vowels together = (24 × 2) = 48 ways
Total arrangements of all letters
= 5!
= (5 × 4 × 3 × 2 × 1)
= 120
Number of arrangements not having vowels together
= (120 - 48)
= 72

In how many different ways can the letters of the word ‘BAKERY’ be arranged?

A) 2400 B) 2005 C) 720 D) 5040 E) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

The letters of the word 'BAKERY' be arranged in 6! ways
= 6!
= 6 × 5 × 4 × 3 × 2 × 1
= 720

In how many different ways can the letters of the word DAILY be arranged?

A) 48 B) 60 C) 120 D) 160 E) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

The given word contains 5 letters, all different.
∴ Required number of ways
= 5!
= 5 × 4 × 3 × 2 × 1
= 120

In how many different ways can letters of the word OFFICES be arranged?

A) 2520 B) 5040 C) 1850 D) 1680 E) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

The given word contains 7 letters of which F is taken 2 times.
∴ Required number of ways
$$\eqalign{ & = \frac{{7!}}{{2!}} \cr & = \frac{{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}}{{2 \times 1}} \cr & = 2520 \cr} $$

In how many different ways can the letters the word FORMULATE be arranged?

A) 8100 B) 40320 C) 153420 D) 362880 E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

The given word contains 9 letters, all different.
∴ Required number of ways
$$\eqalign{ & = {}^9{P_9} \cr & = 9! \cr & = \left( {9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \right) \cr & = 362880 \cr} $$

In an examination there are three multiple choice questions and each question has 4 choices. The number of ways in which a student can fail to get all answer correct is-

A) 11 B) 27 C) 12 D) 63

Discuss

Answer & Solution

Answer: Option D

Solution:

Number of ways of attempting 1^st, 2^nd, 3^rd question are each.
Total number of ways
4³ = 4 × 4 × 4 = 64
Number of ways, getting correct answers = 1³ = 1
∴ Number of ways of not getting all answer correct = 64 - 1 = 63