LAST TIME REVISION COMBINATION

1) Find the value of 
a) ¹⁰C₄.         210

b) ⁹C₇.           36

c) ¹¹C₉ + ¹¹C₈           220

d) If ²⁵Cₓ = ²⁵C₂ₓ₊₁ , find the value of ⁿC₅.        56

e) If ⁿPₓ = 504 and ⁿCₓ =84, find n and x.     9,3

f) ¹³C₀.       1

g) ²⁰C₁      20

h) ˣCₓ.       1

i)  ¹⁵C₁₂       455

j)  ¹²C₇ + ¹²C₆ .         1716

k) ¹¹C₆ + ¹⁰C₅ + ¹⁰C₄      924

l) If ⁿC₂ =21, find n.               7

m) If ²ⁿC₄ : ⁿC₃ = 35:2 then n is.          4

n) If ²⁰C₃ₙ = ²⁰C₂ₙ₊₅. Then n is..       5 or 3

o) If ⁿCₓ : ⁿCₓ₊₁ : ⁿCₓ₊₂ = 1:2:3, n and x are.   14,4

p) value of 3. ⁿ⁺¹C₄ if x= ⁿC₂ .            ˣC₂ 

q) value of ⁿCₓ + ⁿ⁻¹Cₓ₋₁ + ⁿ⁻¹ₓ₋₂ is.             ⁿ⁺¹Cₓ

2) In a meeting there are 10 ladies and 15 gentlemen. A sub-committee consisting of 3 ladies and 5 gentlemen is to be formed. In how many different ways , the sub-committee can be formed ?     360360

3) How many words are different letters, each consisting of two vowels and 3 consonants can be formed from 4 vowels and 7 consonants ?     25200

4) At  an election there are 5 candidates and 3 members are to be elected and a voter is entitled to vote for any number to be elected. In how many ways may a voter choose his vote?       25

5) A question paper contains 12 questions , divided into 3 parts. Part A contains 6 questions , part B and C contains 3 questions each. A candidate is required to attempt 6 questions, selected at least 3 questions from part A and at least one from each of the part B and C. In how many ways can the candidate select his 6 questions ?   495

6) There are n points in a plane, of which no 3 are collinear except m which are collinear . Find the number of 
a) straight lines.         m(m+1)/2 + 1
b) triangles formed by the joining the points.        ⁿC₃ - ᵐC₃

7) A man has 7 friends. In how many ways may he invite 1 or more of them to a party ?      127

8) How many different factors can 210 have?      15

9) A person has in his bag 40 notes of Rs10 each, 9 notes of Rs5 each, 4 notes of Rs2 each and 7 notes of Rs1 each . In how many different ways can he contribute to a  charitable fund ?    5999

10) In how many ways can 8 different things be divided into groups of 5 and 3 ?    56

11) In how many ways can 8 different things be divided equally into two groups?   35

12) In how many ways can 8 oranges of different sizes divided equally between two boys ?    70

13) In how many ways can the crew of a ten-oared boat be arranged if 3 of the crew can row only on the stroke side and 2 can draw only on the bow side?    144000

14) Find the number of 
a);combination 
b) permutation 
in the letters of the word ACCOUNTANCY taken 4 at a time.      35, 1422

15) From 10 candidates, How many selections of 5 can be made so as to
a) include both the youngest and the oldest is the oldest.    56
b) exclude the youngest if it includes the oldest?     196

16) How many triangles can be formed by joining the angular points of a decagon? How many diagonals will it have?      120, 35

17) From 8 boys and 5 girls, how many different selections can be made so as to include at least one boy and one girl ?     7905

18) How many different factors can 2160 have?     39

19) How many four-digit numbers can be formed from the digits 1,1,2,2,3,3,4,5 ?   354

20) If n straight lines be drawn in a plane, no two of them being parallel and no three of them concurrent, how many points of intersection will be there ?     n(n -1)/2

21) if n parallel straight lines in a plane are intersected by a family of m parallel lines, how many parallelograms are there in the network thus formed?    mn/4  (m-1)(n -1)

22) If 20 straight lines be withdrawn in a plane, no two of them being parallel and no 3 of them concurrent, how many points intersection will be there ?    190

23) n points are in space, no 3 of which are collinear. If the number of straight lines and triangles, with the given points only as the vertices, option by joining them are equal, find the value of n.             5

24) How many words each consisting of 5 different letters can be formed by taking 3 consonants from 17 different consonants and 2 vowels from 5 different vowels ?  816000

25) A person has got 20 acquaintances of whom 12 are relatives. In how many ways he may invite 13 guests so that 9 of them would be relatives and one his best friend?   7700

26) In how many ways can three mangoes be selected from 10 mangoes so as always to include a particular mango?     36

27) In how many ways can a committee of three ladies and 4 gentlemen be appointed from a meeting consisting of 8 ladies and 7 gentlemen? What will be the number of ways if Mrs. X refuses to serve in a committee if Mr. Y is a member?   1960, 1540

28) An executive committee of 6 is to be formed from 4 ladies and 7 gentlemen. In how many ways can this be formed When the committee contains 
a) only two ladies members.        210
b) at least two lady members.    371

29) A committee of 5 is to be formed from 6 ladies and 4 gentlemen. In how many ways can this be done so that the committee contains
a) at least two ladies.     246
b) atmost two ladies.      66

30) A box contains 12 lamps of which 5 are defective. In how many ways can a sample of 6 be selected at random from the box so as to include at most 3 defective lamps?  812

31) A candidate is required to answer 6 out of 12 questions which are divided into two groups each containing 6 questions and he is permitted to attempt not more than 4 from any group. In how many different ways can he make up his choice?    850

32) From 7 commerce and 3 science students in how many ways a committee of 5 students can be formed so as to include at least one science student ?    231

33) In an election there are 7 candidates and four members are to be elected and a voter is entitled to vote for any number to be elected. In how many ways may a voter choose his vote ?        98

34) There are 20 points in a plane of which no 3 are collinear except 5 which are collinear . Find the number 
a) of straight lines.        181
b)  of triangles formed by joining the points.       1130

35) Show that in the number of combinations of 16 things taken 8 at a time, the number of combinations in which a particular things occurs , is equal to the number in which it does not occur.         

36) How many combinatiins can be formed of 8 counters marked 1,2,3,4,5,6,7, 8 taking f
4 of them at a time, that being at least one odd and one even counter in each combination.        68

37) In how many ways can a person contribute to a charitable fund out of 1 ten-rupee, 1 five-rupee, 1 two -rupee and 1 one-rupee notes?        15

38) In how many ways can a person contribute to a charitable fund out of 10 ten-rupee notes and 5 five-rupee notes , 2 two-rupees notes  and 1 one-rupee note ?   395

39) Find the number of 
a) combinations
b) permutations
 in the letters of the word STATISTICS taken 4 at a time.           34, 386

40) Show that there are 136 ways of selecting 4 letters from the word EXAMINATION .  

41) 8 questions are given; each question has an alternative. Prove that the number of ways in which a student can select one or more question is 3⁸ -1.

42) Prove that the total number of selections that can be made out of the letters 'daddy did a deadly deed' in 1919.           

43) In how many ways can 9 things be divided in to three groups containing 2, 3 and 4 things respectively.      1260

44) In how many ways can 12 different things be divided into four groups ?    15400

45) In how many ways can 12 orenges of different sizes be divided equally among 4 boys ?         369600

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