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AP Intermediate 1st Year Permutations and Combinations — practice questions

Explore 16 free Permutations and Combinations questions in AP Intermediate 1st Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Permutations and Combinations questions and exercises with answers

Showing questions 1–16 of 16.

The value of $5!$ is:Read the answer and worked solution →The number of ways to arrange $n$ distinct objects in a row is:Read the answer and worked solution →How many different 4-digit numbers can be formed using the digits $1, 2, 3, 4, 5$ without repetition?Read the answer and worked solution →In how many ways can a committee of $3$ persons be chosen from a group of $10$ people?Read the answer and worked solution →The number of ways to arrange the letters of the word 'EXAM' isRead the answer and worked solution →The factorial of a non-negative integer $n$, denoted $n!$, is defined asRead the answer and worked solution →Find the number of arrangements of all the letters in the word 'CAT'.Read the answer and worked solution →Find the number of distinct arrangements of all the letters in the word 'MISSISSIPPI'.Read the answer and worked solution →How many ways can 5 people be seated around a CIRCULAR table?Read the answer and worked solution →From a group of 8 people, how many ways can a COMMITTEE of 3 be selected?Read the answer and worked solution →In how many ways can the letters of the word 'TRIANGLE' be arranged such that all the VOWELS are TOGETHER?Read the answer and worked solution →How many distinct 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6 (each digit can be used at MOST once)?Read the answer and worked solution →The number of ways to select 2 boys and 3 girls from a group of 5 boys and 4 girls isRead the answer and worked solution →Find the number of ways a person can travel from city A to city C if there are 3 routes from A to B and 2 routes from B to C.Read the answer and worked solution →$\binom{n}{r} + \binom{n}{r-1}$ equalsRead the answer and worked solution →How many DIAGONALS does a regular DECAGON (10-sided polygon) have?Read the answer and worked solution →

Worked practice questions

The value of $5!$ is:

  1. $120$
  2. $60$
  3. $720$
  4. $25$
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Correct answer: A. $120$

Factorial definition: $n! = n \times (n-1) \times (n-2) \times \ldots \times 1$. $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$. Quick reference: $4! = 24$, $5! = 120$, $6! = 720$ (option D is $6!$, not $5!$). Factorials grow fast.

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The number of ways to arrange $n$ distinct objects in a row is:

  1. $2^n$
  2. $n$
  3. $n!$
  4. $n^2$
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Correct answer: C. $n!$

Arrangements of $n$ distinct objects in a row: $n$ choices for the first position then $n-1$ for the second, $n-2$ for the third, etc. By the multiplication principle: $n \times (n-1) \times \ldots \times 1 = n!$ For 5 books on a shelf: $5! = 120$ arrangements. For 10 students in a line: $10! = 3,628,800$.

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How many different 4-digit numbers can be formed using the digits $1, 2, 3, 4, 5$ without repetition?

  1. $24$
  2. $120$
  3. $20$
  4. $625$
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Correct answer: B. $120$

We need to arrange 4 digits chosen from 5 distinct digits with no repetition. That's $^5 P_4$: $^5 P_4 = \dfrac{5!}{(5-4)!} = \dfrac{120}{1} = 120$. Alternative count by positions: 5 choices for the thousands digit then 4 for hundreds, then 3 for tens, then 2 for units. $5 \times 4 \times 3 \times 2 = 120$ ✓. Option B (625) would be allowed repetition: $5^4 = 625$. Option C is just $4!$ ignoring the choice of digits to use.

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More Mathematics topics

Sets and RelationsBinomial TheoremLimits and DerivativesLinear InequalitiesSequences and SeriesStraight Lines and Conic SectionsTrigonometric FunctionsComplex Numbers and Quadratic Equations