Advertisements
Advertisements
Question
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
Advertisements
Solution
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is nr.
Explanation:
Number of permutations of n different things taken r at a time
When reception is allowed = filling r places with the help of n different objects when reception is allowed
= n × b × n ... r times
= nr
APPEARS IN
RELATED QUESTIONS
Evaluate 4! – 3!
Compute `(8!)/(6! xx 2!)`
Find n if n – 1P3 : nP4 = 1 : 9
Find x in each of the following:
Which of the following are true:
(2 +3)! = 2! + 3!
Which of the following are true:
(2 × 3)! = 2! × 3!
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
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:
P(6, 4)
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 six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
The number of ways to arrange the letters of the word CHEESE are
The product of r consecutive positive integers is divisible by
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
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
The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
Evaluate the following.
`(3! + 1!)/(2^2!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are divisible by 4?
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
DANGER
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
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
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
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.
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.
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
