Q.1 How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4 without repetition?
24
12
18
36
Explanation - Number of ways = 4P3 = 4 × 3 × 2 = 24.
Correct answer is: 24
Q.2 In how many ways can the letters of the word 'BANK' be arranged?
12
24
48
6
Explanation - Total letters = 4. Arrangements = 4! = 24.
Correct answer is: 24
Q.3 How many ways can 5 people be seated in a row?
25
60
120
720
Explanation - Seating arrangements = 5! = 120.
Correct answer is: 120
Q.4 How many ways can a committee of 2 be chosen from 6 people?
12
15
30
20
Explanation - Ways = 6C2 = 6×5/2 = 15.
Correct answer is: 15
Q.5 In how many ways can the letters of 'LEVEL' be arranged?
30
60
120
240
Explanation - 5 letters with L repeated twice, E repeated twice. Ways = 5! / (2!×2!) = 30.
Correct answer is: 30
Q.6 How many different 5-digit numbers can be formed using digits 1–5 without repetition?
60
120
240
720
Explanation - Ways = 5! = 120.
Correct answer is: 120
Q.7 How many different words can be formed from the letters of 'SCHOOL'?
720
360
540
600
Explanation - 6 letters with O repeated twice. Ways = 6! / 2! = 720/2 = 360.
Correct answer is: 360
Q.8 How many 4-digit numbers can be formed from digits 1,2,3,4,5 if repetition is allowed?
625
120
256
625
Explanation - Each place has 5 choices. Total = 5^4 = 625.
Correct answer is: 625
Q.9 How many ways can 3 boys and 2 girls be seated in a row if boys sit together?
72
144
48
60
Explanation - Treat 3 boys as a block: (3! ways) × 2! for girls × arrangements of 3 units = 3!×2!×3! = 72.
Correct answer is: 72
Q.10 How many ways can you select 2 balls from 6 red and 4 green balls?
45
36
30
25
Explanation - Total balls = 10. Ways = 10C2 = 45.
Correct answer is: 45
Q.11 From 8 men and 6 women, how many committees of 3 can be formed?
364
560
1820
200
Explanation - Total 14 people. Ways = 14C3 = 364.
Correct answer is: 364
Q.12 How many words can be formed using all letters of 'DELHI'?
60
120
240
720
Explanation - 5 distinct letters. Arrangements = 5! = 120.
Correct answer is: 120
Q.13 In how many ways can the letters of 'ACCOUNT' be arranged?
720
2520
5040
3600
Explanation - 7 letters with C repeated twice. Ways = 7!/2! = 5040/2 = 2520.
Correct answer is: 2520
Q.14 How many ways can 4 cards be chosen from a deck of 52?
270,725
52,360
12,870
13,260
Explanation - Ways = 52C4 = 270,725.
Correct answer is: 270,725
Q.15 How many diagonals can a polygon with 10 sides have?
35
45
55
65
Explanation - Diagonals = nC2 – n = 10C2 – 10 = 45–10 = 35.
Correct answer is: 35
Q.16 In how many ways can a team of 11 be formed from 15 players?
1365
5005
3003
6435
Explanation - Ways = 15C11 = 1365.
Correct answer is: 1365
Q.17 How many 4-digit numbers divisible by 5 can be formed using digits 0-9 without repetition?
3024
4536
2720
1440
Explanation - Last digit = 0 or 5. Case-wise count gives total 2720.
Correct answer is: 2720
Q.18 How many permutations of the word 'STATISTICS' are there?
50400
25200
100800
45360
Explanation - 10 letters with S(3), T(3), I(2). Ways = 10!/(3!×3!×2!) = 50400.
Correct answer is: 50400
Q.19 How many 3-digit odd numbers can be formed using digits 1, 3, 5, 7, 9 without repetition?
24
60
120
36
Explanation - Last digit odd (5 choices). Remaining 2 from 4 digits = 4P2 = 12. Total = 5×12 = 60.
Correct answer is: 60
Q.20 In how many ways can 12 identical balls be distributed into 3 distinct boxes?
91
78
66
120
Explanation - Using stars and bars: (12+3-1)C(3-1) = 14C2 = 91.
Correct answer is: 91
Q.21 How many ways can you arrange 7 books on a shelf?
720
5040
40320
120
Explanation - Arrangements = 7! = 5040.
Correct answer is: 5040
Q.22 How many ways can 6 different flowers be placed in 3 vases if vases are distinct and any vase can hold any number?
243
729
512
216
Explanation - Each flower has 3 choices. Total = 3^6 = 729.
Correct answer is: 729
Q.23 How many arrangements of 'MISSISSIPPI' are possible?
34650
34600
34620
34680
Explanation - 11 letters with M(1), I(4), S(4), P(2). Ways = 11!/(4!×4!×2!) = 34650.
Correct answer is: 34650
Q.24 How many ways can 4 balls be chosen from 6 red and 5 blue?
210
330
495
715
Explanation - Total balls = 11. Ways = 11C4 = 330.
Correct answer is: 330
Q.25 How many different 4-digit numbers can be formed using digits 1–9 if repetition is not allowed?
3024
4536
5040
6561
Explanation - Ways = 9P4 = 9×8×7×6 = 3024.
Correct answer is: 3024