हिंदी

In How Many Ways Can a Football Team of 11 Players Be Selected from 16 Players? How Many of These Willinclude 2 Particular Players?

Advertisements
Advertisements

प्रश्न

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?

Advertisements

उत्तर

Number of ways in which 11 players can be selected out of 16 =\[{}^{16} C_{11} = \frac{16!}{11! 5!} = \frac{16 \times 15 \times 14 \times 13 \times 12}{5 \times 4 \times 3 \times 2 \times 1} = 4368\]

 

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 17: Combinations - Exercise 17.2 [पृष्ठ १५]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 17 Combinations
Exercise 17.2 | Q 4.1 | पृष्ठ १५

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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


How many chords can be drawn through 21 points on a circle?


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?


Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.


Compute:

 L.C.M. (6!, 7!, 8!)


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 three-digit odd numbers are there?


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?


Evaluate the following:

n + 1Cn


f 24Cx = 24C2x + 3, find x.


If nC4 , nC5 and nC6 are in A.P., then find n.


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.


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?


Find the number of diagonals of , 1.a hexagon


In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?


In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?


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?


How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?


If 20Cr = 20Cr−10, then 18Cr is equal to


In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?


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


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


Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3


In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?


A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw


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?


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?


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 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 three girls.


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


The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.


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 ______.


Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.


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.


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

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.


The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×