Selection Questions with Solutions — Set 8 (Q71 to Q80)

This set contains Selection and Combination Questions with Solutions — Set 8 (Q71-Q80) 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.

71. How many 2 digit numbers exist whose number of factors is 8?

72. How many natural numbers less than 1000 will have exactly 3 factors?

73. A fruit basket has ‘k’ different types of fruit and each type has ‘n’ number of fruits. In how many ways at least 1 fruit can be selected from the fruit basket?

74. A team of 11 players has to be selected from 20 players which has 5 bowlers. IN how many ways this can be done if at least 4 bowlers are always selected?

75. A class has total 10 students: 6 boys and 4 girls, in how many ways we can select a team of 5 so that number of boy is always more than the number of girls?

76. How many teams of 9 players an be made from 30 players if Ankit, Mohit and Neeraj can not be selected together?

77. 8 students has to be selected such that 4 students from science group & 4 students from Arts group. Number of participants in different group is as follows:-
Science group:- Total 9 students – 5boys and 4 girls
Art group:- Total 9 students – 4 boys and 5 girls
How many ways group of 8 students can be selected if it has 4 boys and 4 girls?

78. A class has 10 students. In how many ways 4 students can be selected if a particular student amit is selected ‘x’ times and out of those ‘x’ times another student Rohit came ‘y’ times with Amit. By what percentage ‘x’ is more than ‘y’?

79. In the previous question if a prticular student Amit came with Rohit but not with shyamu then find the number of ways to select 4 students out of 10 students.

80. A class has 30 students out of which 23 are boys & 7 are girls. In how many ways 15 students can be selected if 5 seats are reserved for girls student?

71. How many 2 digit numbers exist whose number of factors is 8?
Solution:-

If N = aᵖbᑫcʳ…..
then number of factors = (p+1)(q+1)(r+1)………
we are given that number of factors = 8
∴ (p+1)(q+1)(r+1)……. = 8
we have following cases:-

case(i).
If we take 8 = 2×2×2 then number will be in the format a¹b¹c¹, the two digit numbers in this format are

case(ii):-
If we take 8 as 2×4 then number will be in the format a¹b³, the two digit numbers in this format are:

case(iii).
If we take 8 = 1×8, then number will be in the format a⁷ but NO two digit number exist that is in this format

Hence total number of required numbers = 5 + 5 = 10          Answer

72. How many natural numbers less than 1000 will have exactly 3 factors?
Solution:-
Only square of a prime number has three factors, So the number are:
2², 3², 5², 7², 11², 13², 17², 19², 23², 29², 31²
above numbers are less than 1000 & each one has 3 factors
Hence there are 11 desired numbers.   Answer

73. A fruit basket has ‘k’ different types of fruit and each type has ‘n’ number of fruits. In how many ways at least 1 fruit can be selected from the fruit basket?
Solution:-
0 or more fruits can be selected from type 1 in (n+1) ways
0 or more fruits can be selected from type 2 in (n+1) ways
⋮
⋮
⋮
⋮
0 or more fruits can be selected from type k in (n+1) ways
Hence number of ways to select 0 or more fruits = (n+1)ᵏ
Hence total number of ways to select at least 1 fruit
= (n+1)ᵏ – 1     Answer

74. A team of 11 players has to be selected from 20 players which has 5 bowlers. IN how many ways this can be done if at least 4 bowlers are always selected?
Solution:-

Number of ways 
= 4 Bowlers 7 other player + 5 Bowlers ^ other players
= ⁵C₄×¹⁵C₇ + ⁵C₅×¹⁵C₆         Answer

75. A class has total 10 students: 6 boys and 4 girls, in how many ways we can select a team of 5 so that number of boy is always more than the number of girls?
Solution:-

∴ Number of ways = 3B2G + 4B1G + 5B0G
= ⁶C₃×⁴C₂ + ⁶C₄×⁴C₁ + ⁶C₅×1       Answer

76. How many teams of 9 players an be made from 30 players if Ankit, Mohit and Neeraj can not be selected together?
Solution:-
Without any restriction 9 players an be selected from 30 players in ³⁰C₉ ways & when Ankit, Mohit & Neeraj are always selected then 9 players teams can be made in ²⁷C₆ ways.

∴ required number of ways = ³⁰C₉ – ²⁷C₆      Answer

77. 8 students has to be selected such that 4 students from science group & 4 students from Arts group. Number of participants in different group is as follows:-
Science group:- Total 9 students – 5boys and 4 girls
Art group:- Total 9 students – 4 boys and 5 girls
How many ways group of 8 students can be selected if it has 4 boys and 4 girls?
Solution:-
Following different cases can be made:-

Hence total number of ways
 = 1 + 400 + 3600 + 1600 + 25
= 5626 ways         Answer

78. A class has 10 students. In how many ways 4 students can be selected if a particular student amit is selected ‘x’ times and out of those ‘x’ times another student Rohit came ‘y’ times with Amit. By what percentage ‘x’ is more than ‘y’?
Solution:-
total students = 10

& we ae to select 4 students
x = ⁹C₃ = 84
& y = ⁸C₂ = 28
∴      \(\frac{{x – y}}{y} \times 100\% = \frac{{84 – 28}}{{28}} \times 100\% = \frac{{56}}{{28}} \times 100\% = 200\% \)

So x is 200% more than y          Answer

79. In the previous question if a prticular student Amit came with Rohit but not with shyamu then find the number of ways to select 4 students out of 10 students.
Solution:-
Number of ways = ¹⁰⁻²⁻¹C₄₋₂
= ⁷C₂
= 21    Solution

80. A class has 30 students out of which 23 are boys & 7 are girls. In how many ways 15 students can be selected if 5 seats are reserved for girls student?
Solution:-
5G×10B + 6G×9B + 7G×8B
= ⁷C₅ײ³C₁₀ + ⁷C₆ײ³C₉ + ⁷C₇ײ³C₈     Answer

✅ Well done on completing Set 8!

Continue practising with Selection and Combination Questions 81 to 90 → Set 9 or revisit the Selection and Combination 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 Combination (Mathematics) on Wikipedia before attempting the next set.

This page is part of our complete series of Selection and Combination Question 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.