Advertisements
Advertisements
प्रश्न
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 professor is included.
Advertisements
उत्तर
Clearly, 2 professors and 3 students are selected out of 10 professors and 20 students, respectively.
Required number of ways =\[{}^{10} C_2 \times^{20} C_3 = \frac{10}{2} \times \frac{9}{1} \times \frac{20}{3} \times \frac{19}{2} \times \frac{18}{1} = 51300\]
If a particular professor is included, it means that 1 professor is selected out of the remaining 9 professors.Required number of ways =\[{}^{20} C_3 \times^9 C_1 = \frac{20}{3} \times \frac{19}{2} \times \frac{18}{1} \times \frac{9}{1} = 10260\]
APPEARS IN
संबंधित प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
Compute:
L.C.M. (6!, 7!, 8!)
From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?
How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?
Since the number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`
How many 3-digit numbers are there, with distinct digits, with each digit odd?
Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?
Evaluate the following:
12C10
Evaluate the following:
35C35
If 15C3r = 15Cr + 3, find r.
If α = mC2, then find the value of αC2.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
Find the number of diagonals of (ii) a polygon of 16 sides.
How many triangles can be obtained by joining 12 points, five of which are collinear?
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 (i) no girl?
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?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
If n + 1C3 = 2 · nC2 , then n =
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
There are 8 doctors and 4 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.
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
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 how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?
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?
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 at least one boy and one girl
A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.
A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ______.
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 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.
