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
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.
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?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
Compute:
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?
A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
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?
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
How many 9-digit numbers of different digits can be formed?
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?
Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?
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 15C3r = 15Cr + 3, find r.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
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 football team of 11 players be selected from 16 players? How many of these will
include 2 particular players?
Find the number of (ii) triangles
Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?
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 parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
If 20Cr + 1 = 20Cr − 1 , then r is equal to
If C (n, 12) = C (n, 8), then C (22, n) is equal to
If nCr + nCr + 1 = n + 1Cx , then x =
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
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
The number of diagonals that can be drawn by joining the vertices of an octagon is
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
Find the value of 20C16 – 19C16
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red
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 no girls
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
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 ______.
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 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 ______.
