# Permutation and Combination Questions with Answers: Download PDF > Fifteen permutation and combination questions with answers, each starting from the one decision that settles it: does order matter? Free PDF, no sign-up. Source: https://computeprep.com/questions/permutation-and-combination --- ## Permutation and combination questions with answers Permutation and combination questions are settled by one decision made before any arithmetic: does order matter? A committee does not care about order; a seating plan does. Each walkthrough below states that decision first and then counts, which is the sequence that keeps this family from being guesswork. [Download the PDF — 15 questions with answers](https://computeprep.com/questions/permutation-and-combination.pdf) Free, ungated, no email. This is the permutation and combination questions with answers PDF — the same 15 questions as below, with every worked solution at the back, ready to print. ### How to use this set The 15 questions below are ordered the way an exam block is rather than easiest-first: two gentle openers, then a run of medium, and a hard one every sixth question — 2 of the 15 sit in the hard band. Every question is a permutation & combination. Work each question on paper before you open its solution. The walkthrough is the method itself, step for step, so reading it first turns a practice set into a reading exercise and teaches nothing. If you are stuck on the method rather than on one question, the method guide is a better place to start than the next question: [Permutation or combination: does order matter?](https://computeprep.com/drill-types/permutation-combination). ### 15 permutation and combination questions with answers Every question below was generated by the same engine that mints the ComputePrep daily timed drill, and machine-checked before it reached this page — a multiple-choice question validates its own answer against its own options at generation, and ships only with a walkthrough attached. The walkthrough is the engine's own. #### Question 1 In how many different ways can they be arranged? 5 students are to stand in a single row for a photograph. - 120 - 126 - 24 - 25 - 20 - Each position is filled in turn: 5 choices, then 4, and so on down to 1. - Arrangements = 5! = 5 × 4 × 3 × 2 × 1 = 120. - Answer: 120. #### Question 2 In how many ways can it be done? A committee of 2 members is to be formed from 8 people. - 56 - 28 - 16 - 58 - 21 - A committee has no order — SELECTIONS, so use nCr, not nPr. - 8C2 = 8P2 ÷ 2! = 56 ÷ 2 = 28. - Answer: 28. #### Question 3 How many distinct arrangements are there? Consider all arrangements of the letters of the word "GREEN". - 30 - 61 - 120 - 60 - 24 - "GREEN" has 5 letters with one letter repeated twice — divide by 2! for the repeat. - Arrangements = 5! ÷ 2! = 120 ÷ 2 = 60. - Answer: 60. #### Question 4 How many distinct arrangements are there? Consider all arrangements of the letters of the word "PLANET". - 733 - 726 - 36 - 120 - 720 - All 6 letters of "PLANET" are different, so every ordering is distinct. - Arrangements = 6! = 720. - Answer: 720. #### Question 5 How many distinct arrangements are there? Consider all arrangements of the letters of the word "FRIEND". - 722 - 120 - 724 - 732 - 720 - All 6 letters of "FRIEND" are different, so every ordering is distinct. - Arrangements = 6! = 720. - Answer: 720. #### Question 6 In how many ways can the team be chosen? A team of 2 men and 3 women is to be chosen from 4 men and 4 women. - 10 - 34 - 288 - 56 - 24 - Choose each group separately, then MULTIPLY (both choices happen together). - 4C2 × 4C3 = 6 × 4 = 24. - Answer: 24. #### Question 7 In how many ways can it be done? A committee of 2 members is to be formed from 6 people. - 55 - 15 - 12 - 30 - 21 - A committee has no order — SELECTIONS, so use nCr, not nPr. - 6C2 = 6P2 ÷ 2! = 30 ÷ 2 = 15. - Answer: 15. #### Question 8 In how many different ways can they be arranged? 4 students are to stand in a single row for a photograph. - 8 - 6 - 12 - 24 - 16 - Each position is filled in turn: 4 choices, then 3, and so on down to 1. - Arrangements = 4! = 4 × 3 × 2 × 1 = 24. - Answer: 24. #### Question 9 In how many ways can the medals be won? 8 athletes run a race. Gold, silver and bronze medals are awarded. - 512 - 56 - 336 - 348 - 24 - The three medals are DIFFERENT, so order matters — use nPr, not nCr. - 8P3 = 8 × 7 × 6 = 336. - Answer: 336. #### Question 10 How many distinct arrangements are there? Consider all arrangements of the letters of the word "GREEN". - 30 - 60 - 20 - 24 - 120 - "GREEN" has 5 letters with one letter repeated twice — divide by 2! for the repeat. - Arrangements = 5! ÷ 2! = 120 ÷ 2 = 60. - Answer: 60. #### Question 11 How many distinct arrangements are there? Consider all arrangements of the letters of the word "SUMMER". - 366 - 720 - 360 - 373 - 120 - "SUMMER" has 6 letters with one letter repeated twice — divide by 2! for the repeat. - Arrangements = 6! ÷ 2! = 720 ÷ 2 = 360. - Answer: 360. #### Question 12 In how many ways can the medals be won? 7 athletes run a race. Gold, silver and bronze medals are awarded. - 35 - 210 - 21 - 42 - 180 - The three medals are DIFFERENT, so order matters — use nPr, not nCr. - 7P3 = 7 × 6 × 5 = 210. - Answer: 210. #### Question 13 In how many ways can it be done? A committee of 3 members is to be formed from 6 people. - 20 - 10 - 120 - 22 - 18 - A committee has no order — SELECTIONS, so use nCr, not nPr. - 6C3 = 6P3 ÷ 3! = 120 ÷ 6 = 20. - Answer: 20. #### Question 14 In how many ways can it be done? A committee of 2 members is to be formed from 6 people. - 29 - 15 - 35 - 27 - 30 - A committee has no order — SELECTIONS, so use nCr, not nPr. - 6C2 = 6P2 ÷ 2! = 30 ÷ 2 = 15. - Answer: 15. #### Question 15 How many distinct arrangements are there? Consider all arrangements of the letters of the word "GARDEN". - 36 - 120 - 721 - 30 - 720 - All 6 letters of "GARDEN" are different, so every ordering is distinct. - Arrangements = 6! = 720. - Answer: 720. ### Where these questions come from Most free practice for this topic is a scanned upload or a blog quiz, and neither can tell you a question has exactly one answer. That is the one thing this set can promise: it is minted, not typed. The engine behind it serves ComputePrep's daily timed drill, so the questions here are the same shape as the ones a live round would give you — and there is an unlimited supply of them, which is why this page can be regenerated rather than padded. If you want the method rather than more questions, [Permutation or combination: does order matter?](https://computeprep.com/drill-types/permutation-combination) covers the approach, the traps and a worked table. This page and that one deliberately answer different questions: that one is *how do I solve these*, this one is *give me permutation and combination questions with the answers*. ### FAQ #### How do I tell a permutation from a combination? Ask whether swapping two chosen items produces a different outcome. Selecting three people for a committee — no. Seating three people in three chairs, or picking a president and a secretary — yes. Words like arrange, order and rank signal permutation; select, choose and committee signal combination. #### How do I handle "at least" in a selection question? Either sum the cases or subtract the complement, whichever is shorter. "At least two of five" is faster as total minus the zero and one cases. Count how many cases each route needs before you start — that comparison usually saves more time than the arithmetic does. #### What about arrangements with repeated letters? Divide by the factorial of each repeat count. The arrangements of BANANA are 6! divided by 3! for the As and 2! for the Ns, giving sixty. Forgetting a divisor produces a number several times too large, which is exactly what the distractor options are. ### More question banks - [Probability questions with answers](https://computeprep.com/questions/probability) — 15 worked questions and a PDF. - [Mensuration questions with answers](https://computeprep.com/questions/mensuration) — 15 worked questions and a PDF. - [Fast calculation questions with answers](https://computeprep.com/questions/fast-calculation) — 15 worked questions and a PDF. - [All drill types](https://computeprep.com/drill-types) — the method guides behind every bank. ComputePrep is not affiliated with IBPS, SBI, SSC or RBI.