Advertisements
Advertisements
प्रश्न
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.
विकल्प
True
False
उत्तर
This statement is True.
Explanation:
The candidate may attempt in following manner
| Group A | 2 | 3 | 4 | 5 |
| Group B | 5 | 4 | 3 | 2 |
So, the number of attempts of 7 questions
= 6C2 × 6C5 + 6C3 × 6C4 + 6C4 × 6C3 + 6C5 × 6C2
= 2[6C2 × 6C5 + 6C3 × 6C4]
= 2 [15 × 6 + 20 × 15]
= 2[90 + 300]
= 2 × 390
= 780.
APPEARS IN
संबंधित प्रश्न
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
How many three-digit numbers are there with no digit repeated?
How many three-digit odd numbers are there?
If 15C3r = 15Cr + 3, find r.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
Find the number of diagonals of (ii) a polygon of 16 sides.
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (ii) at least one boy and one girl?
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
If 20Cr = 20Cr−10, then 18Cr is equal to
If 20Cr = 20Cr + 4 , then rC3 is equal to
If 15C3r = 15Cr + 3 , then r is equal to
If mC1 = nC2 , then
If 43Cr − 6 = 43C3r + 1 , then the value of r is
The number of diagonals that can be drawn by joining the vertices of an octagon is
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
If n + 1C3 = 2 · nC2 , then n =
Find the value of 15C4
The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
| C1 | C2 |
| (a) One book of each subject; | (i) 3968 |
| (b) At least one book of each subject: | (ii) 60 |
| (c) At least one book of English: | (iii) 3255 |
If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.
