English

From a Group of 15 Cricket Players, a Team of 11 Players is to Be Chosen. in How Many Ways Can this Be Done?

Advertisements
Advertisements

Question

From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?

Advertisements

Solution

Required number of ways =\[{}^{15} C_{11}\]

Now,

\[{}^{15} C_{11} =^{15} C_4\]
\[= \frac{15}{4} \times \frac{14}{3} \times \frac{13}{2} \times \frac{12}{1} \times^{11} C_0\]
= 1365  
shaalaa.com
  Is there an error in this question or solution?
Chapter 17: Combinations - Exercise 17.2 [Page 15]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.2 | Q 1 | Page 15

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

If nC8 = nC2, find nC2.


Determine n if  `""^(2n)C_3 : ""^nC_3 = 12 : 1`


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?


A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?


There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?


A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?


How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?


How many different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?


If nC4 = nC6, find 12Cn.


If 18Cx = 18Cx + 2, find x.


If n +2C8 : n − 2P4 = 57 : 16, find n.


If 28C2r : 24C2r − 4 = 225 : 11, find r.


If 2nC3 : nC2 = 44 : 3, find n.


Find the number of diagonals of (ii) a polygon of 16 sides.


In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?


Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.


Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.


If C (n, 12) = C (n, 8), then C (22, n) is equal to


If mC1 nC2 , then


5C1 + 5C2 5C3 + 5C4 +5C5 is equal to


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


Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.


There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.


Ten students 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 or not in the project. Find the number of possible selections.


Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.


A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?


A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?


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 ______.


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 must all be of the same colour.


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


Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.


The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is ______.


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 ______.


A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.


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 ______.


From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×