Advertisements
Advertisements
प्रश्न
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
Advertisements
उत्तर
Two particulars books are never selected from 10 books. So, 4 books need to be selected from 8 books.
Required number of ways if two particular books are never selected =\[{}^8 C_4 = \frac{8}{4} \times \frac{7}{3} \times \frac{6}{2} \times \frac{5}{1} = 70\]
APPEARS IN
संबंधित प्रश्न
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
How many three-digit numbers are there with no digit repeated?
How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?
If 8Cr − 7C3 = 7C2, find r.
If 2nC3 : nC2 = 44 : 3, find n.
If 16Cr = 16Cr + 2, find rC4.
If α = mC2, then find the value of αC2.
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
include 2 particular players?
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular student is excluded.
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
How many triangles can be obtained by joining 12 points, five of which are collinear?
Find the number of (i) diagonals
Find the number of (ii) triangles
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: exactly 3 girls?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?
The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together 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
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
Find the value of 80C2
Answer the following:
A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
If α = mC2, then αC2 is equal to.
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
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
In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?
The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is ______.
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.
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 |
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
