Advertisements
Advertisements
प्रश्न
In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.
उत्तर
First we take books of a particular subject as one unit.
Thus there are 4 units which can be arranged in 4! = 24 ways.
Now in each of arrangements
Mathematics books can be arranged in 3! ways,
History books in 4! ways,
Chemistry books in 3! ways
And biology books in 2! ways.
Thus the total number of ways = 4! × 3! × 4! × 3! × 2! = 41472.
APPEARS IN
संबंधित प्रश्न
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
Find n if n – 1P3 : nP4 = 1 : 9
Find r if `""^5P_r = 2^6 P_(r-1)`
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Which of the following are true:
(2 × 3)! = 2! × 3!
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
Evaluate each of the following:
8P3
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 6 men and 5 women can dine at a round table if no two women sit together ?
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
English alphabet has 11 symmetric letters that appear same when looked at in a mirror. These letters are A, H, I, M, O, T, U, V, W, X and Y. How many symmetric three letters passwords can be formed using these letters?
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 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
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
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
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.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is ______.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
