English

How Many Different Selections of 4 Books Can Be Made from 10 Different Books, Iftwo Particular Books Are Always Selected; - Mathematics

Advertisements
Advertisements

Question

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

Solution

Two particular books are selected from 10 books. So, 2 books need to be selected from 8 books.
Required number of ways if 2 particular books are always selected =\[{}^8 C_2 = \frac{8}{2} \times \frac{7}{1} = 28\]

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

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.2 | Q 8.2 | Page 16

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


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?


Compute: 

(i)\[\frac{30!}{28!}\]


In how many ways can an examinee answer a set of ten true/false type questions?


There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?


How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?


How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?


Evaluate the following:

14C3


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


From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?


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?


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.


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?


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 a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?


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? 


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: at least 3 girls?


Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines


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 20Cr + 1 = 20Cr − 1 , then r is equal to


If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to


Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?


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


If n + 1C3 = 2 · nC2 , then n =


Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120


There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?


Answer the following:

A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?


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?


If nC12 = nC8, then n is equal to ______.


Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red 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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×