Permutation and Combination Miscellaneous Exercise 3
1 A college of offers 5 courses in the morning and the three in the evening. The number of ways a student can select exactly one course, either in the morning or in the evening.
a)5 B)3 C)8 D)15
Answer-
Number of ways of selecting one course from 8 available course
(i.e., 5 courses in morning and 3 in the evening)= 5+3 = 8
2) A college as 7 courses in the morning and 3 in the evening the possible number of choices with the student if he wants to study one course in the morning and one in the evening is
A)21 B)4 C)42 D)10
Answer-
A college has 7 course in the morning 3 in the evening
possible number choices for one course in morning and one course in evening
(7 `\times` 3)
=21
3) In how many ways can a student and 8 Indian 4 American and 4 English man has can be set seated in a row so that all person of the same nationality sit together?
A) 3!8! B) 3!4!8!4! C) 4! D)8!4!4!
Answer-
8 Indians take take their seats in 8! ways 4
4 Americans take their seats in 4! ways 4
4 English man take their seats 4! ways 4
Three groups English,
Americans, and Englishmen can be permuted in 3! ways
Required number= `3! \times 8! \times 4! \times 4!`
4) In how many ways can 10 examination papers be arranged so that the best and the worst paper never come together?
A)9 x 8! B)8 x 8! C) 9×9! D)8×9!
Answer-
D) suppose, best and worst paper come together, 2 (best+worst)=1 unit
now we have with us (10-2)=8 papers
now, 8 papers+1 papers = 9 papers
arranging 9 papers = 9!
Arrangement where worst and best paper come together = 9! `\times` 2!
Total permutation of 10 papers = 10!
Total arrangement where best and worst paper never come together
=10! - 9!2!
=10.9! - 9!2!
=9!(10-2)
=9! `\times` 8
5) In how many ways for boys and 3 girls can be seated in a row so that they are alternate.
A) 12 B) 288 C) 144 D) 256
5) Find the number of triangles which can be formed by joining the angular points of a polygon of its sides as vertices.
A) 16 B) 56 C)24 D) 8
7) A question paper has two parts a and b is containing to 10 questions. If a student has to choose 8 pass from part A and v from part B in how many ways can he choose the questions?
A) 320 B)750 C)40 D)113408
8) There are 10 persons among whom to our brothers. The total number of ways in which this person can be seated around a table so that exactly one person sits between the brothers former is equal to
A)2!×7! B) 2!×8! C) 3!×7! D)3!×8!
9) The number of arrangement of the letter of the word Banana is in which two ends do not appear adjacently
A)80 B)60 C)40 D)100
10) The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two females are not seated together is a need for
A)840 B)600 C)720 D)480
ll) answer the following question
1) Find the value of r if
{56}^P_{r+2}:{54}P_{r-1}=30800:2
2)How many words can be formed by writing letters in the world CROWN in different order?
3)Find the number of words that can be formed by using all the letters in the word remain if this was written in dictionary order what will be the 40 word ?
4)Capital English alphabet has 11 symmetric letters that appear CM when looked at in a mirror. These letters R A h I m O T u v w X and by how many symmetry three letter password can be formed using these letters?
5) How many numbers are formed using the digits 3,2,04,3,2,3 exceed 1 million?
6) Ten student are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project.Find the number of possible
selections.
7) A student finds 7 books of his interest but can borrow only three books. He wants to borrow chemistry part 2 book only if chemistry part 1 can also be borrowed. Find the number of ways you can read free books that he wants to borrow.
8)30 objects are to be divided into three groups containing 71013 object in stock find the number of distinct ways for doing so.
9) A student passes an examination if he secure a minimum of in each of the seven subjects full stop find the number of ways a student can say.
10) 9 friends decide to go for a picnic into groups. One group decides to go by her and the other group decide to provider in find the number of different ways of going so if there are must be at least three friends in each group.
11) A hall has 12 lamps and every lamp can be switched on independently a. Find the number of ways of illuminating the hall.
12) How many quadratic equation can be formed using number from 0,2,4,5 as coefficients if the coefficient can be repeated in an equation.
13) How many 6 digit telephone numbers can be formed of the first two digits are 45 and no digit can appear more than once?
14)A question paper 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
15)find the number of ways of dividing 20 objects in three groups of sizes 8 7 and 5.
16)There are four doctors and eight lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.
17) 4 parallel lines intersect another set of 5 parallel lines. Find the number of distinct parallelograms are formed.
18) There are 12 distinct points A,B,C,..., L, in order, on a circle. Lines are drawn passing through each pair of points
I)How many lines are parallel
II) How many lines pass through D
III)How many triangles are determined by lines.
IV)How many triangles have on vertex C.
 |
| Permutation and Combination Miscellaneous Exercise 3 |
Permutation and Combination Miscellaneous Exercise 3
