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;

Advertisements

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?


How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?


Prove that

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

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 3-digit numbers are there, with distinct digits, with each digit odd?


A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.


If nC4 = nC6, find 12Cn.


If 15Cr : 15Cr − 1 = 11 : 5, find r.


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


In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?


In how many ways can a football team of 11 players be selected from 16 players? How many of these will

 exclude 2 particular players?


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 excluded.


There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.


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? 


Find the number of (ii) triangles


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 ways in which : (a) a selection


A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?


There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.


If 15C3r = 15Cr + 3 , then r is equal to


If nCr + nCr + 1 = n + 1Cx , then x =


5C1 + 5C2 5C3 + 5C4 +5C5 is equal to


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


If α = mC2, then αCis equal to.


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?


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


If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.


A convex polygon has 44 diagonals. Find the number of its sides.


Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is ______.


If some or all of n objects are taken at a time, the number of combinations is 2n – 1.


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!)`.


The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×