This set contains Permutation or Arrangement Questions with Solutions — Set 1 (Q1-Q10) covering a mix of question types and difficulty levels — from basic to advanced — exactly as asked in real competitive exams.
Solutions are written in a simple, step-by-step notebook style for easy self-study and quick understanding. Each solution is broken down step by step so even the toughest question feels easy. These questions are hand-picked for students preparing for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and all campus placement aptitude tests. International students preparing for GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests will find these equally useful.
✏️ Attempt each question on your own first — then check the solution below.
Permutation or Arrangement Questions 1 to 10 with Solutions
1. In how many ways 15 students can be seated on 20 seats in a row ?
2. In how many ways 5 distinct volume of chemistry and 7 distinct volume of Botany book can be arranged on a bookshelf such that no two chemistry books are together ?
3. In how many ways 15 students can be arranged in a row ?
4. In how many ways 8 prizes from 1ˢᵗ to 8ᵗʰ can be given to a group of 8 students that includes 4 boys & 4 girls. Here a student can get only 1 prize ?
5. In how many ways 12 boys and 10 girls can be arranged in a straight line such that all the girls and all the boys are together?
6. In how many ways 4 pens can be given to 8 students if each student can get any number of prizes ?
7. In how many ways batting order of 11 players can be made out of 15 players ?
8. In how many ways 5 distinct volume of chemistry & 7 distinct volume of chemistry books can be arranged on a bookshelf ?
9. In how many ways 5 distinct volume of chemistry & 7 distinct volume of botany books can be arranged on a bookshelf such that all the botany books are together ?
10. In how many ways 5 distinct volumes of chemistry & 7 distinct volume of botany books can be arranged on a bookshelf such that no two botany books are together ?
Permutation or Arrangement Questions 1 to 10 — Step-by-Step Solutions
1. In how many ways 15 students can be seated on 20 seats in a row ?
Sol:-
First select then arrange
15 seats can be selected out of 20 seats in ²⁰C₁₅ ways. Now 15 students can be arranged in these 15 seats in 15! ways.
Hence total number of ways = ²⁰C₁₅.15! Answer
2. In how many ways 5 distinct volume of chemistry and 7 distinct volume of Botany book can be arranged on a bookshelf such that no two chemistry books are together ?
Sol:-
•B₁•B₂•B₃•B₄•B₅•B₆•B₇•
7 distinct botany books can be arranged in 7! ways. This will create 8 spaces, marked by •(dot), to place chemistry book.
Now 5 chemistry books can be arranged in these 8 places in ⁸C₅.5! ways.
Hence total number of ways = (7!).(⁸C₅.5!) Answer
3. In how many ways 15 students can be arranged in a row ?
Sol:- 15 students can be arranged in a row in 15! ways Answer
4. In how many ways 8 prizes from 1ˢᵗ to 8ᵗʰ can be given to a group of 8 students that includes 4 boys & 4 girls. Here a student can get only 1 prize ?
Sol:- Here we are to arrange 8 distinct prizes at 8 distinct places (8 distinct students).
which can be done in 8! ways Answer
In this question the sentence ‘4 boys & 4 girls’ is irrelevant only thing that matters is 8 students i.e. 8 different places.
5. In how many ways 12 boys and 10 girls can be arranged in a straight line such that all the girls and all the boys are together ?
Sol:-
12 boys in themselves can be arranged in 12! ways.
10 girls in themselves can be arranged in 10! ways.
now these two bunches can be arranged in 2! ways.
Hence total number of ways = 12!.10!.2! Answer
6. In how many ways 4 pens can be given to 8 students if each student can get any number of prizes ?
Sol:- 1ˢᵗ pen can be given to any student.
Hence 1ˢᵗ pen can be given in 8 ways.
2ⁿᵈ pen can be given to any student.
Hence 2ⁿᵈ pen can be given in 8 ways
.
.
.
.
.
Similarly, 4ᵗʰ pen can be given in 8 ways
Hence total number of ways = 8×8×8×8
= 8⁴ Answer
7. In how many ways batting order of 11 players can be made out of 15 players ?
Sol:- First select then arrange.
11 Players can be selected out of 15 players in ¹⁵C₁₁ ways.
Now these 11 players can be arranged in 11! ways.
Hence total number of ways = ¹⁵C₁₁.11! Answer
8. In how many ways 5 distinct volume of chemistry & 7 distinct volume of chemistry books can be arranged on a bookshelf ?
Sol:- Here all 12 articles are different & we are to arrange them.
which can be done in 12! ways Answer
9. In how many ways 5 distinct volume of chemistry & 7 distinct volume of botany books can be arranged on a bookshelf such that all the botany books are together?
Sol:-
∴ total number of ways to arrange =
10. In how many ways 5 distinct volumes of chemistry & 7 distinct volume of botany books can be arranged on a bookshelf such that no two botany books are together ?
Sol:-
•C₁•C₂•C₃•C₄•C₅•
From above figure we have 6 places (marked by •) to place 7 botany books.
So there is no arrangement possible to place botany books such that no two botany books are together.
Hence No arrangement possible Answer
✅ Well done on completing Set 1!
Continue practising with Permutation or Arrangement Questions 11 to 20 → Set 2 or revisit the Permutation or Arrangement Concept Page to strengthen your formulas and tricks before moving ahead.
Consistent practice is the key to mastering Selection and Combination for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and international exams including GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests. Want to understand the concept better? Read about Permutation (Mathematics) on Wikipedia before attempting the next set.
This page is part of our complete series of Selection and Combination Questions with solutions for competitive exams — covering every question type from basic to advanced so you can build speed, accuracy and confidence. Practising these questions regularly will also strengthen your core LCM and HCF concept before your exam day.