This set contains Division and Distribution of Objects into Groups 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.
Division and Distribution of Objects into Groups Questions 1 to 10 with Solution
1. In how many ways 30 identical chocolates be distributed among 5 students ?
2. In how many ways 30 students can be send to 5 class rooms ?
3. In how many ways 20 different article can be distributed equally among 4 persons ?
4. In how many ways 30 identical chocolates be distributed among 5 students such that a particular student Ankit receive at least 1 chocolate ?
5. In how many ways 30 identical chocolates be distributed among 5 students such that each student receive at least 1 chocolate ?
6. In how many ways 30 identical chocolates be distributed among 5 students such that each student receive at least 2 chocolates ?
7. In how many ways 30 identical chocolates be distributed among 5 students ?
8. Ankit has 15 friends to invite, in how many ways can he send invitation cards to them if there are three different courier services available ?
9. In how many ways 50 bananas can be distributed to 5 students ?
10. In how many ways 50 bananas can be distributedd to 5 students such that each of them receive at least 5 bananas?
Division and Distribution of Objects into Groups Questions ━ 1 to 10 Step-by-Step Solutions
1. In how many ways 30 identical chocolates be distributed among 5 students ?
Sol:-
identical object ━ distinct group
number of ways to distribute = ³⁰ ⁺ ⁴C₄
= ³⁴C₄ Answer
2. In how many ways 30 students can be send to 5 class rooms ?
Sol:-
∴ number of ways = 5³⁰ Answer
3. In how many ways 20 different articles can be distributed equally among 4 persons ?
Sol:-
distinct object ━ distinct group
┃
Group size fixed
┃
Group size are equal
∴ Number of ways of division = \(\frac{{20!}}{{5!5!5!5!}} \times \frac{1}{{4!}}\)
Number of ways to distribute = \(\left( {\frac{{20!}}{{5!5!5!5!}} \times \frac{1}{{4!}}} \right)\) × 4!
= \(\boldsymbol{\frac{{20!}}{{{{\left( {5!} \right)}^4}}}}\) Answer
4. In how many ways 30 identical chocolates be distributed among 5 students such that a particular student Ankit receive at least 1 chocolate ?
Sol:- identical chocolate ━ distinct group
5. In how many ways 30 identical chocolates be distributed among 5 students such that each student receive at least 1 chocolate ?
Sol:- identical chocolate ━ distinct group
6. In how many ways 30 identical chocolates be distributed among 5 students such that each student receive at least 2 chocolates ?
Sol:- identical object ━ distinct group
7. In how many ways 30 identical chocolates be distributed among 5 students ?
Sol:- identical object ━ distinct group
Number of ways = 5³⁰ Answer
8. Ankit has 15 friends to invite, in how many ways can he send invitation cards to them if there are three different courier services available ?
Sol:-
1ˢᵗ friend can be invited in 3 ways
2ⁿᵈ friend can be invited in 3 ways
Similarly,
.
.
.
.
.
.
15ᵗʰ friend can be invited in 3 ways
Hence total number of ways to invite = 3×3×3×………..15 times
= 3¹⁵ Answer
9. In how many ways 50 bananas can be distributed to 5 students ?
Sol:- identical objects ━ distinct groups
10. In how many ways 50 bananas can be distributedd to 5 students such that each of them receive at least 5 bananas ?
Sol:- identical object ━ distinct group
✅ Well done on completing Set 1!
Continue practising with Division and Distribution of Objects into Groups Questions 11 to 20 → Set 2 or revisit the Division and Distribution of Objects into Groups 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.
This page is part of our complete series of Permutation 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.