Advertisements
Advertisements
प्रश्न
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
पर्याय
True
False
उत्तर
This statement is False.
Explanation:
Arrangement of n things, r taken at a time in which m things occur together.
So, number of object excluding m object = (r – m)
Here, we first arrange (r – m + 1) object
∴ Number of arrangements = (r – m + 1)!
m objects can be arranged in m! ways
So, the required number of arrangements = (r – m + 1)! × m!
APPEARS IN
संबंधित प्रश्न
Evaluate 4! – 3!
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 words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
Find x in each of the following:
Which of the following are true:
(2 +3)! = 2! + 3!
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
How many six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?
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?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
If n is a positive integer, then the number of terms in the expansion of (x + a)n is:
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
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?
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
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
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
GARDEN
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?
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.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
