25.
Permutations & Combinations
1. If nC2 = nC3, then nC4 is. given question in a paper, when each question has an
(a) 2 (b) 3 alternative is:
(c) 5 (d) 4 (a) 28-1 (b) 2 × 82
2. If 35Cn+7 = 35C4n – 2 , then n =? (c) 3 8 (d) 38 - 1
(a) 28 (b) 3, 6 16. Number of ways in which a mixed doubles tennis game
(c) 3 (d) 6 can be arranged b/w 10 players consisting of 6 men and 4
3. There are 4 letters boxes in a post office. In how many women is
ways can a man post 8 distinct letters (a) 180 (b) 90
(a) 8× 8 (b) 84 (c) 48 (d) 12
(c) 48 (d) 8P4 17. Number of different ways in which a man can invite one a
4. Number of ways in which 4 men and 4 women can be more of his 6 friends to dinner is:
seated at round table so that no two women may be (a) 15 (b) 30
together is: (c) 63 (d) 120
(a) 576 (b) 48 18. There are 10 true false questions. Number of ways ,in
(c) 16 (d) 144 which they can be answer is:
5. If n-1 C6 + n-1 C7>nC6 then. (a) 10! (b) 10
(a) n > 4 (b) n > 12 (c) 210 (d) 102
(c) n ≥ 13 (d) n >13 19. A lady gives a dinner party for 6 guests. Number of ways
6. Number of possible out comes when a coin is tossed five in which they may be selected among 10 friends if two of
times: the friends will not attend the party together is:
(a) 25 (b) 52 (a) 112 (b) 140
5 (c) 164 (d) not
(c) 10 (d) 2
20. The figures 4,5,6,7,8 are written in every possible order.
7. Number of ways in which a student choose 5 course out of
The number of distinct numbers greater than 56000 is:
9, when 2 course are compulsory is:
(a) 72 (b) 90
(a) 35 (b) 25
(c) 96 (d) 98
(c) 45 (d) 95
21. In an examination a student has to answers 4 questions
8. There are 4 letters and 4 direct envelopes. Number of
out of 6. Number of ways in which the student can make
ways in which every letter be put into a wrong envelope
choice is:
is:
(a) 4 (b) 6C4
(a) 8 (b) 16
(c) C2
6 (d) 6
(c) 15 (d) 9
22. In how many ways can 7 toys be given to 3 children when
9. Sum of digits in the unit place of all the number’s formed
each child is eligible for all toys?
with the help of 3,4,5,6 taken all at a time is:
(a) 3570 (b) 4350
(a) 18 (b) 108
(c) 2187 (d) 2426
(c) 432 (d) 144
23. Number of triangles that can be formed with 6 points on a
10. In an examination there are 3 MCQ and each question has
circle is:
4 choices. Number of sequences in which student can fail
(a) 6 (b) 20
to get all answers correct is:
(c) 15 (d) 12
(a) 11 (b) 15
24. Number of arrangements which can be made by using all
(c) 80 (d) 63
the letters of the word LAUGH if the vowels are adjacent
11. A polygon has 44 diagonals. Number of its sides are:
is:
(a) 10 (b) 11
(a) 10 (b) 24
(c) 12 (d) 13
(c) 120 (d) 48
12. Six identical coins are arranged in a row. Number of ways
25. Number of ways in which 4 faces of a regular tetrahedron
in which the number of tails is equal to number of heads
can be painted with 4 different colors is:
is:
(a) 4! (b) 4
(a) 20 (b) 120
(c) 1 (d) not
(c) 9 (d) 40
26. Number of distinct number which can be formed by using
13. Number of 2 digit even number that can be formed form
any no of digits 0,1,2,3,4 but using each not more than
the digits 1, 2, 3, 4 and 5. (repetition not allowed)
once in each number is:
(a) 8 (b) 5!
(a) 261 (b) 356
(c) 26 (d) 16
(c) 410 (d) 96
14. A five digit number divisible by 3 is to be formed by using
27. Number of ways in which 10 persons can go in two boats
the number 0, 1, 2, 3, 4, 5 without repetitions. The total
,so that there may be 5 on each boat, supposing that two
number of ways in which this can be done is:
particular persons are not going in the same boat is:
(a) 216 (b) 600 1 1
(c) 240 (d) 3125 (a)210C5 (b) 28C5
15. Number of all possible selections which a student can (c) 2×8C4 (d)8C4
make for answers any one or more questions out of eight
SCO 224, Level -2, sector 37-B, Chandigarh. Ph.:0172-4187465
25. Permutations & Combinations
28. Number of ways in which ‘n’ ties can be selected form a 35. Number of ways of selecting 10 players out of 22 when 4
rack displaying ‘3n’ different ties is: of them being excluded and 6 always included is:
3𝑛! (a) 22C10 (b) 12C2
(a) (b) 3×n!
2𝑛!
3𝑛! (c) 495 (d) not
(c) 3n! (d)𝑛! 2𝑛!
36. Maximum number of points of intersection 8 circles.
29. Number of all four digit number’s with distinct digits is: (a) 16 (b) 24
(a) 9999 (b) 4536 (c) 28 (d) 56
(c) 10P4 (d) 9P4 37. Maximum number of points of intersection of 8 straight
30. Number of ways in which 6(+) and 4(-) sings can be lines.
arranged in a line such that no two (-) signs occur (a) 8 (b) 16
together is: (c) 28 (d) 56
(a) 10C4 (b) 10P4 38. Maximum number of points in which 4 circles and 4
(c) C4
7 (d) not straight lines intersect.
31. Number of ways in which 8 different flowers can be (a) 26 (b) 50
strung to form a garland so that 4 particular flowers are (c) 56 (d) 72
never separated. 39. Number of straight lines that can be drawn out of 10
(a) 4! 4! (b) 288 points of which 7 are collinear is:
8!
(c) (d) 5! 4! (a) 24 (b) 23
4!
32. Number of ways of arranging the letters (c) 25 (d) 21
AAAAABBBCCCDEEF in a row when no two C’s are 40. In a cricket championship there are 36 matches. Total
together is: number of teams, if each plays one match with other :
15! 15! 13! (a) 8 (b) 9
(a) − 3! (b) −
5! 3! 3! 2! 5! 3! 3! 2! 5! 3! 2! (c) 10 (d) not
12! 13 𝑃 3 12!
(c) 5! 3! × (d) 5! 3! 2! × 13P3 41. In an examination, a candidate is required to pass four
2! 3!
33. On a railway route there are 15 stations. Number of different subjects. The number of ways he can fail is:
tickets required in order that it may be possible to book a (a) 4 (b) 10
passenger form every station to every other is: (c) 15 (d) 24
15! 42. Given 5 line segments of length 2,3,4,5,6 units, then
(a) (b) 15!
2
15! 15! number of ∆’s that can be formed by joining these lines :
(c) 13! (d) 13! 2! (a) 5 C3 (b) 5C3 - 3
34. Number of ways in which 9 students can be equally (c) C3 - 2
5 (d) 5C3 - 1
distributed among 3 section: 43. Number of diagonals in an octagon is:
9! (a) 20 (b) 28
(a) 9! (b)
3! 3 (c) 8 (d) 16
9!
(c) (d) None of these 44. Number of ways in which 6 faces of a cube be painted
3! 3! 3
with 6 different colors is :
(a) 6! (b) 6
(c) 6C2 (d) not
Ans Key
(1-10) cbcdd aadbd
(11-20) baaad bccbb
(21-30) bcbdc acdbd
(31-40) bccdc dcbcb
(41-44) cbad
SCO 224, Level -2, sector 37-B, Chandigarh. Ph.:0172-4187465
