हिंदी

From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. - Mathematics

Advertisements
Advertisements

प्रश्न

From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

योग
Advertisements

उत्तर

Out of 25 students, 10 students are to be included in the tour group. But 3 out of 10 students are like this

(i) When all three join the touring party or

(ii) All three do not happen.

(i) Methods of selecting the excursion group when three students join the team = 22C7

(ii) Methods of selection when all three students are not included in the tour group = 22C10

Methods of selecting the touring party in both the cases = 22C7 + 22C10

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Permutations and Combinations - Miscellaneous Exercise [पृष्ठ १५७]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 7 Permutations and Combinations
Miscellaneous Exercise | Q 10 | पृष्ठ १५७

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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?


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?


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`


In how many ways can six persons be seated in a row?


How many 9-digit numbers of different digits can be formed?


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 18Cx = 18Cx + 2, find x.


If 15C3r = 15Cr + 3, find r.


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


How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?


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 included.


How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;


A student has to answer 10 questions, choosing at least 4 from each of part A and part 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 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? 


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? 


How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?


A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?


If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =


There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is


How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120


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?


All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.


In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.


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 three girls.


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


In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is ______.


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!)`.


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 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

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


There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.


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?


There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×