Advertisements
Advertisements
Question
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
Advertisements
Solution
Required ways of selecting 4 books from 10 books without any restriction =\[{}^{10} C_4 = \frac{10}{4} \times \frac{9}{3} \times \frac{8}{2} \times 7 = 210\]
APPEARS IN
RELATED QUESTIONS
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
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?
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?
In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?
If 15C3r = 15Cr + 3, find r.
If α = mC2, then find the value of αC2.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
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
include 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 included.
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
How many triangles can be obtained by joining 12 points, five of which are collinear?
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 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: exactly 3 girls?
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?
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
If 43Cr − 6 = 43C3r + 1 , then the value of r is
Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.
The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
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 ______.
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 from the lot.
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
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 include 2 particular players?
If nC12 = nC8, then n is equal to ______.
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.
The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is ______.
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 ______.
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
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 ______.
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.
