Advertisements
Advertisements
प्रश्न
The number of permutation of n different things taken r at a time, when the repetition is allowed is ______.
विकल्प
rn
nr
`(n!)/((n - r)!)`
`(n!)/((n + r)!)`
Advertisements
उत्तर
The number of permutation of n different things taken r at a time, when the repetition is allowed is nr.
Explanation:
The correct answer is nr because when repetition is allowed, each of the r positions can be filled by any one of the n different objects. Thus, the total number of possible permutations is n × n × ... × n = nr.
APPEARS IN
संबंधित प्रश्न
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Find r if `""^5P_r = 2^6 P_(r-1)`
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
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
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
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
The number of 5-digit telephone numbers having atleast one of their digits repeated 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! |
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
