Selection & Combination Questions with Solutions — Set 2 (Q11 to Q20)

This set contains Selection and Combination Questions with Solutions — Set 2 (Q11-Q20) 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.

11. What is the number of ways in which three numbers in A.P. can be selected from the given set {1, 2, 3, 4, 5,…………120}?

12. What is the number of ways in which three numbers in A.P. can be selected from the given set {1, 2, 3, 4, 5, ……….. , 121}?

13. Let there are 8 oranges, 6 mangoes & 3 apples
(i) How many selection of fruits can be made?
(ii) How many selection of fruits can be made such that at least 1 apple is always included?
(iii) How many selection of fruits can be made such that at least one fruit of each type is always included?

14. In how many ways 7 players can be selected out of 15 players if Virat is always included?

15. In how many ways at least 5 players can be selected from a group of 7 players?

16. In how many ways a team of p students can be selected from q students such that r student are always included & s students are always included?

17. If a bus conductor has 435 different tickets then findd the number of stoppage that the bus has, consider only one way journey.

18. A student is allowed to select atmost n books from a collection of (2n + 1) books. what is the number of ways of doing this?

19. How many factors of N = 2⁵×3⁵×5⁵×7⁵×11⁵ ends with 3 zeros?

20. In how many ways a team of 11 players can be selected from 18 players if out of 18 players, 2 player can play only as wicket keeper.

11. What is the number of ways in which three numbers in A.P. can be selected from the given set {1, 2, 3, 4, 5,…………120}?
Solution:-

The given set {1, 2, 3, 4, 5, ……….., 120} has 60 even & 60 odd integers.
Now let three numbers be a, b, c which are in A.P.
then

so (a + c) is also even & this can happen by 2 ways:-

12. What is the number of ways in which three numbers in A.P. can be selected from the given set {1, 2, 3, 4, 5, ……….. , 121}?
Solution:-

The given set { 1, 2, 3, 4, 5, ………..121} has  odd &  even integers.
now let three numbers from this set which are in A.P. be a, b, c

13. Let there are 8 oranges, 6 mangoes & 3 apples
(i) How many selection of fruits can be made?
(ii) How many selection of fruits can be made such that at least 1 apple is always included?
(iii) How many selection of fruits can be made such that at least one fruit of each type is always included?
Solution:- 

(i). oranges can be selected in (8 + 1) = 9 ways
mangoes can be selected in (6 + 1) = 7 ways
apples can be selected in (3 + 1) = 4 ways
So number of ways of selecting fruit is = 9×7×4 = 252
this also included 1 case when none of the fruits is selected.

Hence total number of ways of selecting 1 or more fruits is 252 – 1 = 251 Answer

(ii). oranges can be selected in (8 + 1) = 9 ways
mangoes can be selected in (6 + 1) = 7 ways
apples can be selected in 3 ways since at least 1 apple is always included.

So number of ways of selecting fruit is = 9×7×3 = 189 Answer

∴ Number of ways of selecting fruit is = 8×6×3 = 144 Answer

14. In how many ways 7 players can be selected out of 15 players if Virat is always included?
Solution:- 

Sincec Virat is always included
∴ number of ways of selection = ¹⁵⁻¹C₇₋₁
= ¹⁴C₆ Answer

15. In how many ways at least 5 players can be selected from a group of 7 players?
Solution:-

16. In how many ways a team of p students can be selected from q students such that r student are always included & s students are always included?
Solution:-

ᑫ ⁻ ʳ ⁻ ˢCₚ ₋ ᵣ      Answer

17. If a bus conductor has 435 different tickets then findd the number of stoppage that the bus has, consider only one way journey.
Solution:-

if the bus has ‘n’ number of stoppage then to have a ticket we have to select 2 stoppages out of n and that can be done in ⁿC₂ =    = 435
⟹ n = 30
Hence bus has 30 stoppage. Answer

18. A student is allowed to select atmost n books from a collection of (2n + 1) books. what is the number of ways of doing this?
Solution:-

19. How many factors of N = 2⁵×3⁵×5⁵×7⁵×11⁵ ends with 3 zeros?
Solution:-

N = 2⁵×3⁵×5⁵×7⁵×11⁵
N = 2³×5³(2²×3⁵×5²×7⁵×11⁵)

= 3×6×3×6×6
= 1944
these 1944 factors ends with 3 zeros

Hence 1944 Answer

20. In how many ways a team of 11 players can be selected from 18 players if out of 18 players, 2 player can play only as wicket keeper?
Solution:-

From 2 wicket keepers only 1 is selected & this can be done in ²C₁ ways.
And remaining 10 players can be selected from remaining 16 players in ¹⁶C₁₀ ways.
So total number of ways = ²C₁×¹⁶C₁₀ Answer

✅ Well done on completing Set 2!

Continue practising with Selection and Combination Questions 21 to 30 → Set 3 or revisit the Selection and Combination Concept Page to strengthen your formulas and tricks before moving ahead.

Consistent practice is the key to mastering LCM and HCF 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 Combination (Mathematics) on Wikipedia before attempting the next set.

This page is part of our complete series of LCM and HCF 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.