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
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
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.
Compute:
(i)\[\frac{30!}{28!}\]
From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
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?
How many three-digit numbers are there with no digit repeated?
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 different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
Evaluate the following:
n + 1Cn
If 15Cr : 15Cr − 1 = 11 : 5, find r.
If n +2C8 : n − 2P4 = 57 : 16, find n.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
How many triangles can be obtained by joining 12 points, five of which are collinear?
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
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
If C (n, 12) = C (n, 8), then C (22, n) is equal to
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is
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
Find the value of 15C4 + 15C5
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?
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 ______.
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?
How many committee of five persons with a chairperson can be selected from 12 persons.
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
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.
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.
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.
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 ______.
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 ______.
