Advertisements
Advertisements
Question
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
Advertisements
Solution
Number of maths book = 4
Number of physics books = 3
Number of chemistry books = 2
Number of biology books = 1
Since we want books of the same subjects together
We have to treat all maths books as 1 unit
All physics books as 1 unit
All chemistry books as 1 unit
And all biology books as 1 unit.
Now the total number of units = 4
They can be arranged in 4! ways.
After this arrangement.
4 maths book can be arranged in 4! ways
3 physics book can be arranged in 3! ways
2 chemistry book can be arranged in 2! ways
And 1 biology book can be arranged in 1! way
∴ Total Number of arrangements 4! 4! 3! 2! = 6912
APPEARS IN
RELATED QUESTIONS
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
Evaluate each of the following:
P(6, 4)
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
Find x if `1/(6!) + 1/(7!) = x/(8!)`
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
What is the maximum number of different answers can the students give?
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
