Advertisements
Advertisements
प्रश्न
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 |
Advertisements
उत्तर
| C1 | C2 |
| (a) One book of each subject; | (i) 60 |
| (b) At least one book of each subject: | (ii)3255 |
| (c) At least one book of English: | (iii) 3968 |
Explanation:
We have 3 books of Mathematics, 4 of Physics and 5 on English
(a) One book of each subject = 3C1 × 4C1 × 5C1
= 3 × 4 × 5
= 60
(b) Atleast one book of each subject = (23 – 1) × (24 – 1) × (25 – 1)
= = 7 × 15 × 31
= 3255
(c) Atleast one book of English = (25 – 1) × 27
= 31 × 128
= 3986
APPEARS IN
संबंधित प्रश्न
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
Compute:
L.C.M. (6!, 7!, 8!)
In how many ways can an examinee answer a set of ten true/false type questions?
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
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 three-digit numbers are there with no digit repeated?
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`
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?
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?
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 18Cx = 18Cx + 2, find x.
If 15C3r = 15Cr + 3, find r.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
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?
Find the number of diagonals of (ii) a polygon of 16 sides.
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 group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girl?
Find the number of (i) diagonals
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 the selection be made?
If 20Cr = 20Cr + 4 , then rC3 is equal to
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
The value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is
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 and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
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.
There are 8 doctors and 4 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.
Find the value of 15C4 + 15C5
Find the value of 20C16 – 19C16
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?
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is ______.
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.
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 ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
