English

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(Iii) at Least 3 Girls?

Advertisements
Advertisements

Question

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(iii) at least 3 girls? 

Advertisements

Solution

If the team has at least 3 girls, then the number of ways of selecting 5 members =\[{}^4 C_3 \times^7 C_2 +^4 C_4 \times^7 C_1 = 84 + 7 = 91\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 17: Combinations - Exercise 17.2 [Page 16]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.2 | Q 19.3 | Page 16

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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?


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.


How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?


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:

(i) exactly 3 girls?

(ii) atleast 3 girls?

(iii) atmost 3 girls?


Prove that

\[\frac{1}{9!} + \frac{1}{10!} + \frac{1}{11!} = \frac{122}{11!}\]

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 team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?


How many different five-digit number licence plates can be made if

the first-digit cannot be zero, but the repetition of digits is 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?


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:

n + 1Cn


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


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. In how many ways can he choose the 7 questions?


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.


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: atmost 3 girls?


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 nCr + nCr + 1 = n + 1Cx , then x =


5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to


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?


Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is


The number of diagonals that can be drawn by joining the vertices of an octagon is


If n + 1C3 = 2 · nC2 , then n =


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 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.


Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?


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.


Find the value of 20C16 – 19C16 


We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?


How many committee of five persons with a chairperson can be selected from 12 persons.


Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.


The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.


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 ______.


15C8 + 15C9 – 15C6 – 15C7 = ______.


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 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.


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 ______.


Number of selections of at least one letter from the letters of MATHEMATICS, is ______.


The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×